Linear faraday induction generator for the generation of electrical power from ocean wave kinetic energy and arrangements thereof

ABSTRACT

A linear generator includes a permanent magnet array having at least two magnets arranged end-to-end. A set of conductive coils is arranged around the permanent magnet array. A four-phase full wave rectifier is configured to accept alternating current inputs from the set of conductive coils and to produce one or more direct current outputs. A summing circuit is configured to aggregate the one or more direct current outputs from the rectifier to produce a combined, rectified direct current output.

RELATED APPLICATION DATA

This application is a Continuation application of co-pending U.S. patentapplication Ser. No. 14/611,713, filed on Feb. 2, 2015, which in turn isa Continuation application of issued U.S. Pat. No. 8,946,920, filed onDec. 27, 2013 and issued on Feb. 3, 2015, which in turn is a Divisionalapplication of issued U.S. Pat. No. 8,629,572, filed on Oct. 29, 2012and issued on Jan. 14, 2014, all of which are incorporated herein byreference in their entirety.

BACKGROUND

1. Technical Field

The present principles are directed to linear faraday inductiongenerators as well as electrokinetic seawall apparatuses that employlinear faraday induction generators to dissipate ocean wave kineticenergy.

2. Description of the Related Art

Seawalls are widely used to protect fragile beaches, coastline, andcoastal structures from the enormous power and energy of ocean waves andto provide areas of calm water for shipping and recreational purposes.Waves impact upon a seawall, of which there are basically two principaltypes—type 1 seawalls of uniform thickness with a level exposed facethat is perpendicular to the oncoming ocean waves, and type 2 seawallswhose ocean exposed surface is concave upward with a base of significantgreater thickness than at its summit. In either case, the waves collideviolently with the seawall, which then dissipates the wave energythrough frictional losses into useless heat. Seawalls of the first typesuffer from the problem that some of the wave energy is reflectedproducing extremely violent and undesirable standing waves in front ofthe seawall. Seawalls of the second type, developed to avoid thestanding wave problem, suffer from the fact that the curved exposedsurface suffers from increased cumulative damage with shortened lifespanas that type of seawall has to absorb all of the wave energy rather thanreflecting a portion of it back toward the ocean in the direction of theoriginal wave propagation. In either case, tremendous amounts of energyis wasted and lost as frictional heat and turbulence.

This large amount of undesirable wave kinetic energy is capable of beingconverted into electrical power. In an effort to mitigate the effect ofclimate change from carbon emissions from fossil fuel production, otheralternative sources of energy, which include wind, hydrogen, solar,nuclear, cellulosics, geothermal, damming, hydroelectric, tidal current,and ocean wave, are now being explored to supply energy requirements formodern industrialized societies. Ocean wave energy in particular hasbeen investigated for possible use as far back as 1799 with the firstknown patent, and since then, many patents have been issued in anattempt to tap an estimated 1 TW (Terawatt) to 10 TW of power containedin deep water wave power resources of which, by one estimate, 2.7 TW ispotentially practical to tap, thereby providing a significant percentageof the planet's power consumption of 15 TW. With existing technology,however, only about 0.5 TW could in theory be captured.

Energy and momentum is imparted to the surface layer of ocean by windsblowing across its surface by virtue of the shearing frictional forcesof the wind against the water surface. This transfer occurs when thewave produced as a result of this interaction propagates across thesurface at a slower velocity than the wind. This wind ocean system iscalled the “wind sea state.” A given amount of energy transferred perunit of time will produce a wave whose eventual height will depend on 4factors: wind speed, the duration of time the wind has been blowing, thedistance over which the wind excites the waves (known as the fetch), andthe depth and topography of the ocean. Once the wind ceases to blow,these wind generated waves, called ocean surface waves, continue topropagate along the surface of the ocean in the direction of the windthat generated them. The visual distortions that are seen and indicatethe presence of such waves are called swells. Because of the restoringforce of gravity (hence, ocean waves are known as surface gravitywaves), the waves continue to propagate after the wind has ceasedblowing, leaving their point of origin as they travel through a viscousmedium with a given density, namely ocean water. The energy and momentumassociated with an ocean wave front is largely a surface and nearsurface phenomenon. In deep water, water molecules follow circularmotion paths, while in more shallow water, the motions are elliptical.In water depths equal to half the wavelength (the distance betweensuccessive wave crests), this orbital motion declines to less than 5% ofthe motion at the surface. Because of this phenomenon, energy transferby propagating ocean waves occurs at and just below the surface of theocean. Furthermore, the momentum associated with this kinetic energy ofmotion is both linear, reflecting the momentum imparted to the water'ssurface through wind drag forces, and angular, given by the fact thatthe wind applies shearing forces to the water at an angle to itssurface.

There are two wave velocities associated with ocean wave phenomena, thephase velocity and the group velocity. The phase velocity measures howquickly the wave disturbance propagates through the ocean. It refers tothe velocity of each individual wave that propagates across the ocean.However, many waves together may contribute to a summation wave, calleda wave group that in itself propagates over the ocean at its ownseparate velocity. It is the velocity of the wave group, or summationwave, that measures the speed at which energy is transferred across agiven section of ocean. Power and energy is transported at and justunder the ocean surface at the group velocity. In deep water, the groupvelocity is equal to one half the phase velocity whereas in shallowwater, the group velocity is equal to the phase velocity, reflecting thefact that the phase velocities of all of the individual waves decreaseas they approach shallow water in the vicinity of a coastline. Since theenergy, momentum, and power contained in a wave remain constant (lessfrictional losses) as the individual waves approach the coastline, theheight of the wave must increase as its base slows, until it becomesunstable causing the wave to fall over itself, a process call breaking.The process of a wave impinging upon a coastline causes all of itsstored energy to be released as frictional heat resulting in theundesirable effects to the coastline. The seawall intercepts the wavefronts prior to the breaking process and dissipates the energy instead.Also, waves with the longest wavelengths usually have the highest waveheights, travel the fastest in the ocean, and arrive ahead of waves withshorter wave lengths, as seen with the long high swells observed severaldays prior to the arrival of a hurricane. These waves carry the greatestamount of energy and are the most harmful to beaches, coast lines, andthe life expectancies of seawalls.

The power as given by watts per unit length of wave front transmittedthrough a plane vertical to the plane of propagation (ocean surface) andparallel to the wave crest front is dependent on the product of thesquare of the “significant wave height” in meters and the period of thewave in seconds, with the period being the reciprocal of the frequency,which, in turn, varies inversely in a complex function to the wavelengthand ocean depth. The height of the wave is defined as the verticaldistance between the crest and succeeding trough and it is equal totwice the amplitude of the wave. The “significant wave height” is astatistical average of the heights of the one third of the waves withthe highest heights measured during a specified measured time intervalof 20 min to 12 hours. The power being transmitted by the wave is knownas the “wave energy flux” or “wave power” and it is given by thefollowing equation:

$\begin{matrix}{P = {\frac{\rho \; g^{2}}{64\; \pi}H_{t}^{2}T_{e}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

where,

-   -   P=Wave energy flux (wave power), Watts/meter (W/m) of advancing        wave front=Joules/sec/meter (J/s/m)    -   ρ=Density of water, 1000 kg/m    -   H_(t)=“Significant wave height”=average height of highest        one-third of waves measured in a given time interval in meters    -   T_(e)=Period of wave in seconds    -   g=Gravitational acceleration, 9.8 m/s        Equation 1 can be approximated by the equation:

P≈0.5H _(t) ² T _(e) where P is in Kw/m  Eq. 2

Power and energy get transported horizontally at and just under thesurface of the ocean at the group velocity. The above equationscalculate the power available in gravity ocean waves, and the energyassociated with that power may be calculated as well from linear wavetheory, and the thermodynamic principle of the equipartition theorem,applied to a system where the restoring force of gravity causes an oceanwave to function as an harmonic oscillator in which half of its energyon average is kinetic and half is potential. The total average densityof energy in Joules per unit of horizontal area of ocean surface inmeters (J/M) is given by:

$\begin{matrix}{E = {\frac{1}{16}\rho \; {gH}_{t}^{2}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

where,E=Average mean density of gravity ocean wave energy at and just belowthe ocean surface, J/m².For the following equations below,C_(g)=Group velocity (wave envelope velocity), m/s,—energy propagationvelocityC_(p)=Phase velocity, m/s,—individual wave front propagation velocityA=Amplitude of wave—one half the height, in meters, the verticaldistance from crest to succeeding trough.

This power (and energy) gets transported horizontally in the directionof wave propagation at the group velocity. In addition, this power, forwaves traveling in sufficiently deep water that the depth, h=½λ, may becalculated by:

$\begin{matrix}{{P = {EC}_{g}}{{where},}} & {{Eq}.\mspace{14mu} 4} \\{C_{g} = {\frac{g}{4\pi}T_{e}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

Equations 3 and 5 placed into equation 4 gives equation 1, andtherefore, the approximate wave power equation, equation 2, whichmeasures the maximum available wave power or wave energy flux that canbe extracted by an ocean wave extraction device:

$P = {{( {\frac{1}{16}\rho \; {gH}_{t}^{2}} )( \frac{{gT}_{e}}{4\; \pi} )} = {\frac{\rho \; g^{2}}{64\; \pi}H_{t}^{2}T_{e}}}$

The efficiency of the wave energy dissipation device whose interceptionwave surface interface is of length L is given by:

$\begin{matrix}{E_{f} = \frac{P_{ext}}{PL}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

where,

P is given by Eq. 1 or as a good approximation, Eq. 2

E_(f)=Efficiency of the wave energy dissipation device

L=Wave extraction device−wave interception interface length in meters

P_(ext)=Measured electrical power extracted from the device in watts

Finally the generated electrical power density, P_(d), can be computedto measure the density of power generation by the device:

P _(d) =P _(ext) /V  Eq. 7:

where,

P_(d)=Generated power density, W/m³

V=Volume of the energy dissipating device, m³

For illustrative purposes, a calculated example describing the energy inan ocean wave is provided:

A vertically oriented cylindrical shaped power generating device ofdiameter 11 meters and height 44 meters is placed floating so that itsdiameter is parallel to the direction of the arriving wavefront andperpendicular to the direction of propagation of the wave. Further, itis located in deep water a few kilometers off the coast and encounterswaves with a height (“significant wave height”) of 3 meters and a waveperiod of 8 seconds. Using Eq. 2 to solve for P, we obtain:

$P \approx {( {0.5\frac{KW}{m^{3}s}} )( {3m} )^{2}( {8s} )} \approx {36\frac{KW}{m}}$

36 Kw per meter of wavelength incident on the device over an impactlength of 11 meters or 396 Kw in total power. The device produces 150Kw. Its efficiency is 150 Kw/396 Kw or 39% (from Eq. 6). In addition,given that the device is a cylinder of diameter 11 meters and height 44meters, where its volume is V=πr²h or 4180 m³; the power generatingdensity P_(d)=150 Kw/4180 m³=0.36 W/m³ or 360 mw/m³ (from Eq. 7).

Note that because of the dissipated ocean wave energy extracted aselectrical energy by the device, the wave train in back of the devicewill be larger than the attenuated wave front in front of the device.Also, the available wave energy flux increases linearly with the periodof the wave but exponentially with the square of the height whichproduces several effects. Storm waves of great height will destroy suchwave energy dissipating devices. For instance, if an approaching stormled to waves of 15 meters high with a period of 15 seconds impacting thedevice, the device would have to deal with a wave energy flux of 1.7MW/m of wave impact surface on the device with a total wave energy fluxof 18.7 MW. Also, even if the device has excellent survivability, theefficiency of the device will go down drastically if the waves impactingupon it are significantly higher than the height with which the devicewas designed operate.

Thus, all such ocean wave energy dissipating devices extracting theenergy as electrical power should be reasonably efficient through a widerange of ocean wave sizes. It should be durable and have reasonablemaintenance requirements as would be the case in a seawall of aconventional nature that is made out of concrete, steel bulkhead, orheavy boulders stabilized by some means.

The prior art technology has made use of systems including and involvingpistons and pumps using hydraulic fluids and water, spinning turbines,oscillating water columns to produce air pressure changes drivinghydraulic or turbine systems, water intake water elevators with downhillhydroelectric flow turbine systems, linear magnetic arrays coupled tooscillating coil assemblies, and piezoelectric wave pressure toelectrical energy transducers. All of these technologies have beenconsidered or have been attempted to be used in extracting electricalenergy from ocean wave energy.

SUMMARY

A linear generator includes a permanent magnet array having at least twomagnets arranged end-to-end. A set of conductive coils is arrangedaround the permanent magnet array. A four-phase full wave rectifier isconfigured to accept alternating current inputs from the set ofconductive coils and to produce one or more direct current outputs. Asumming circuit is configured to aggregate the one or more directcurrent outputs from the rectifier to produce a combined, rectifieddirect current output.

An array of linear generators includes a plurality of individual lineargenerators, each having a single direct current output. Each of thelinear generators includes a permanent magnet array having at least twomagnets arranged end-to-end, a set of conductive coils arranged aroundthe permanent magnet array, a four-phase full wave rectifier configuredto accept alternating current inputs from each subset of conductivecoils and to produce one or more direct current outputs, and a summingcircuit configured to aggregate the one or more direct current outputsfrom the rectifier to produce a combined, rectified direct currentoutput. The set of conductive coils includes four subsets of a pluralityof conductive coils, with each coil being electrically connected inseries with the other coils in the respective subset of coils.

An array of linear generators includes a plurality of individual lineargenerators, each having a single direct current output. Each of thelinear generators includes a permanent magnet array having at least twomagnets arranged end-to-end, a set of conductive coils arranged aroundthe permanent magnet array, a plurality of four-phase full waverectifiers configured to accept alternating current inputs from arespective subset of four conductive coils and to produce one or moredirect current outputs, and a summing circuit configured to aggregatethe one or more direct current outputs from the rectifiers to produce acombined, rectified direct current output. The set of conductive coilsincludes a plurality of subsets of four conductive coils each.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1A is an illustrative side view diagram of an ElectrokineticSeawall showing an arrangement of repeating Wave Energy Converters(WEC's);

FIG. 1B is a top view of an Electrokinetic Seawall deployed forprotection of a coastline and conventional seawall;

FIG. 1C is a top view of an electrokinetic seawall deployed forprotection of a harbor installation with conventional seawalls;

FIG. 2A is a top view of a two-layered electrokinetic seawall indicatingthe attenuation of waves passing through the array of WEC's (theattached linkages between all adjacent WEC's are not shown for ease ofillustration);

FIG. 2B is a top view of a single WEC positioned in open water;

FIG. 2C is a top view of an open water ringed network of WEC's showingdownstream attenuation of waves passing through it;

FIG. 3A depicts a side view of a repeating WEC component of theElectrokinetic Seawall apparatus at the time of the passage of a wavetrough, where the WEC component is comprised of a Mobile Subunit (halfscale relative to rest of the structure), a Fixed Subunit, a VibrationalEnergy Linear Electric Generator (VLEG), and an Inertial Liquid WaveDampening Stabilizer (ILWDS);

FIG. 3A (1) is an inset showing a section of a stator involved inbraking a rotor in rough seas;

FIGS. 3B (1) and 3B (2) respectively show two embodiments of suspendinga vertically oscillating rotor from the top of a mobile subunit buoyfloatation collar;

FIG. 3C depicts a view of the Mobile Subunit of the WEC showing the useof O rings or piston rings in place of the rubber or silicone bumperring illustrated in FIG. 3A and showing a spring tension adjustmentunit;

FIG. 4A illustrates the magnetic field distribution of an attractingmagnet field pole configuration;

FIG. 4B illustrates the magnetic field distribution of a repellingmagnet field pole configuration;

FIG. 5A shows a Compressive Repulsive Magnetic Field (CRMF) PermanentMagnet Array (PMA) implementation of Compressive Repulsive MagneticField Technology and its associated magnetic field distribution;

FIG. 5B shows a conventional attractive magnetic field PMA and itsassociated magnetic field distribution;

FIG. 5C shows a CRMF PMA implementation of Compressive RepulsiveMagnetic Field Technology employing a threaded central support tube andthreaded magnetic pole pieces;

FIG. 6 shows a variable wire gauge Field Coil Array (FCA) surroundingthe Compressive Repulsive Magnetic Field PMA;

FIG. 7A illustrates (not to scale) a VLEG embodiment 1 composed of a 3Magnetic Unit PMA stator and its associated FCA rotor of length twicethat of the PMA Stator—The first of two exemplary invariantly symmetricembodiments of the VLEG of Order 3 described herein;

FIG. 7B illustrates (not to scale) a VLEG embodiment 2 composed of a 3Magnetic Unit PMA Rotor and its associated FCA Stator of length twicethat of the PMA Rotor—The second of two exemplary invariant embodimentsof the VLEG of Order 1 described herein;

FIG. 8A is an illustrative diagram showing an idealized sinusoidalvertical displacement of the wave with respect to time as it passesthrough a WEC component of the Electrokinetic Seawall apparatus;

FIG. 8B is an illustrative diagram showing the upward positive verticaldisplacement of a PMA rotor (PMA rotor—FCA stator embodiment of theVLEG) with the passage of an ocean wave crest through the WEC;

FIG. 8C is an illustrative diagram showing the neutral zero displacementof the PMA rotor (PMA rotor—FCA stator embodiment of the VLEG) with thepassage of the neutral or zero point of the ocean wave through the WEC;

FIG. 8D is an illustrative diagram showing the downward negativevertical displacement of the PMA rotor (PMA rotor-FCA stator embodimentof the VLEG) with the passage of the ocean wave trough through the WEC;

FIG. 9A shows (to approximate scale) a side view of a basic VibrationalEnergy Electrokinetic Transducer (of matrix order 1), a vibrationalenergy harvester device including the basic VLEG, Embodiment 1,comprising a one magnetic unit PMA Rotor including a 2 magnet, 3 polepiece repulsive pole configuration, two breaking magnets, and a 4 coilvariable wire gauge FCA stator;

FIG. 9B shows (to approximate scale) a side view of the basicVibrational Energy Electrokinetic Transducer (of matrix order 1), avibrational energy harvester device, including the basic VLEG,Embodiment 2, comprising a one magnetic unit PMA Stator including a 2magnet, 3 pole piece repulsive pole configuration, two breaking magnets,and a 4 coil variable wire gauge FCA rotor;

FIG. 9C shows the magnetic field configuration around a two magnet, 3pole piece single magnet unit repulsive pole configuration PMA with nobreaking magnet, depicting wide divergence of the magnetic field at theends of the PMA;

FIG. 9D shows the magnetic field configuration around a two magnet, 3pole piece single magnet unit repulsive pole configuration PMA with twobreaking magnets, depicting the deflection of the end magnetic fieldflux lines back toward the PMA;

FIG. 9E shows a cross-section view from above of the VLEG embodimentcomposed of the PMA rotor and FCA stator;

FIG. 9F shows the VLEG embodiment composed of the PMA stator and FCArotor;

FIG. 9G shows a side view of an alternative structure of the VLEG,embodiment number 1, with an additional repulsive field deflectingmagnet at each PMA rotor end;

FIG. 9H shows a side view of an alternative structure of the VLEG,embodiment number 2, with an additional repulsive field deflectingmagnet at each PMA stator end;

FIG. 10A Depicts (to approximate scale) a side view of a VibrationalEnergy Electrokinetic Matrix Transducer of order 9 that collects anddissipates vibrational wave kinetic energy into electricalenergy—embodiment 1, the preferred embodiment, with 9 (3 shown) singlemagnetic unit PMA rotors in repulsive pole configuration and 9 FCAstators (3 shown);

FIG. 10B depicts a top view of the internal magnetic field of the order9 Vibrational Energy Electrokinetic Matrix Transducer of FIG. 10A;

FIG. 11 depicts the structure of higher order Vibrational EnergyElectrokinetic Matrix Transducers—A 5 PMA×2 PMA by 3 PMA (order 30)three dimensional matrix is shown with extension to higher orders—theassociated FCA's have been omitted for clarity—for preferred embodiment1, where the PMA's are the rotors and the FCA's are the stators;

FIG. 12A illustrates an example in which an Electrokinetic SeawallApparatus is flexibly tethered to an anchor on the seabed using a chain,cable, or spring and with a power takeoff cable, where the individualWEC's are not rigidly attached to each other;

FIG. 12B illustrates an example in which an Electrokinetic SeawallApparatus is rigidly anchored to the seabed by a column, where the powertakeoff cable may either be taken separately to the seabed or through arigid anchoring pole and where the individual WECs are not rigidlyattached to each other;

FIG. 12C illustrates an example in which WEC components of anElectrokinetic Seawall Apparatus are individually and rigidly attachedto a conventional mechanical seawall or bulkhead so that they areessentially components of this conventional mechanical seawall;

FIG. 12D illustrates a side view of an individual Inertial Liquid WaveDampening Stabilizer (ILWDS) of 4 WECs that are rigidly attached to eachother by metal plate brackets;

FIG. 12E(1) illustrates a side view of 4 WEC's, each of whose ILWDS isrigidly bolted to a boat-like partially submerged metal structure thatis neutrally to slightly positively buoyant via sufficient buoyancystructures attached to it;

FIG. 12E(2) illustrates a top view of the 4 WEC's of FIG. 12(E)(1);

FIG. 13A depicts a top view of a square mesh configuration of theElectrokinetic Seawall with its repeating component WEC's in a squaregrid location lattice;

FIG. 13B depicts the individual WEC component of the mesh array of FIG.13A;

FIG. 13C depicts the side oblique view looking slightly down of thesquare mesh configuration of FIG. 13A with its associated tetheredcorner anchors to the seabed;

FIG. 13D depicts a top view of a circular mesh configuration of theElectrokinetic Seawall with its repeating component WEC's in asymmetric, moderately dense spring lattice configuration enclosing andprotecting a structure within;

FIG. 13E depicts a side view of the circular mesh lattice configurationof FIG. 13D;

FIG. 13F depicts a top view of a circular mesh configuration of theElectrokinetic Seawall with its repeating component WEC's in asymmetric, very dense spring lattice configuration enclosing andprotecting a structure within;

FIG. 14 Illustrates a block diagram of a system implementing wavekinetic energy dissipation through conversion to electric energy andtransfer via various embodiments of Power Collection Circuitry (PCC).

FIG. 15A is a schematic diagram of electrical connections for embodiment1 of the VLEG (matrix order 1) with a 4 coil FCA Stator and 2 magnetrepulsive pole single structural magnetic unit PMA Rotor;

FIG. 15B shows the phase relationships of the AC voltage waveformsproduced in each of the 4 coil outputs from the VLEG of FIG. 15A;

FIG. 15C is a schematic diagram of embodiment 1 of power collectioncircuitry (PCC) comprising a conventional 4-phase full wave bridgerectifier resulting in a filtered two terminal DC output voltage thatmay be used with the basic VLEG;

FIG. 15D is a schematic diagram of embodiment 2 of PCC comprising a4-phase full wave rectifier with grounded coil inputs resulting in athree terminal center tapped filtered bipolar DC output voltage that maybe used with the basic VLEG;

FIG. 15E shows an embodiment 3 of PCC comprising a 4 input single phasebridge rectifier network with a current summing aggregating circuitresulting in a filtered two terminal DC output voltage and currentthrough the load whose magnitude is approximately the sum of theindividual filtered DC voltage and current outputs from the four coilsused with the basic VLEG;

FIG. 15F shows embodiment 4 of PCC comprising a four input single phasebridge rectifier network with a voltage summing aggregating circuitresulting in a filtered two terminal DC output voltage through the loadthat is approximately the sum of the voltages of the individual filteredDC voltage outputs of the four coils used with the basic VLEG;

FIG. 16 illustrates a four magnetic unit VLEG PMA with a partially drawnFCA whose coils are series connected in four groups so as to produce a4-phase AC output, the associated PCC of the VLEG PMA, the four possibleshown embodiments for AC to DC power rectification and filtering, and aDC to DC converter and DC to AC inverter;

FIG. 17 depicts a three magnetic unit VLEG PMA with an approximatelydrawn to scale FCA and its associated PCC circuitry comprising sixindividual 4-phase full wave bridge rectifier filter circuits for eachVLEG magnetic unit whose four coils are each connected to the AC inputsof the corresponding bridge rectifier and whose DC outputs of each maybe connected to either a six input DC current summing aggregator circuitor a DC voltage summing aggregator circuit with a final DC voltageoutput;

FIG. 18A illustrates the schematic diagram of the six DC current inputcurrent summing aggregator circuit of FIG. 17 in detail;

FIG. 18B illustrates the schematic diagram of the six DC voltage inputvoltage summing aggregator circuit of FIG. 17 in detail;

FIG. 18C illustrates the DC to AC inverter or DC to DC converter towhich any of the summing circuits of FIGS. 16, 17, 18A, and 18B may beconnected;

FIG. 18D illustrates a schematic diagram of an ultra precisionembodiment of the current summing aggregator circuit illustrated in FIG.18B;

FIG. 19A shows 3 separate VLEGs, each with separate PCC circuits andoutputs as a module representation;

FIG. 19B shows a schematic diagram for the current summing aggregatorcircuit for the three VLEG's of FIG. 19A;

FIG. 19C shows a schematic diagram for the voltage summing aggregatorcircuit for these three VLEG's of FIG. 19A;

FIGS. 20A, 20B, 20C, and 20D illustrate the power output of a VLEG as afunction of ocean wave height, ocean wave period, PMA magnet lineardimensions as volume, and the number of VLEG magnetic structural unitsin the PMA, respectively;

FIGS. 20E and 20F illustrate the power output of a VLEG of a given sizeas a function of the degree of magnetization of the magnets (N factor)and a function of the number of coils in the FCA and the number of VLEGstructural magnetic units in the PMA, respectively; and

FIG. 21 illustrates the phase relationships between the verticaldisplacement of a VLEG rotor and its velocity and the force in to theWEC from the ocean wave, the voltage signal in the VLEG as a function oftime, the mechanical ocean wave kinetic power, P_(M), dissipated by therotor, and the electrical power, P_(E), developed in the VLEG by therelative movement of the rotor with respect to the FCA stator.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present principles relate to apparatus, systems, and methods fordissipation of kinetic energy of ocean surface waves by means ofelectromagnetic Faraday conversion into electrical energy; a seawallemploying electromagnetic means to dissipate ocean waves for the purposeof reducing damage or interference to the operation of conventional seawalls, harbors, coastlines, and structures contained within, includingbuildings, docking facilities, sand dunes and other beach erosionprevention structures. In the process of enhancing and protectingfunctional and recreational uses of a portion of coastline with theemployment of such means of energy conversion inherent to theElectrokinetic Sea Wall (EKS) apparatus described herein, production ofuseful electrical power is accomplished from the otherwise damaging andwasteful kinetic energy of ocean waves.

The present principles, because the ocean wave energy dissipation andelectrical energy extraction is implemented in the form of a seawall inan exemplary embodiment that can be attached to currently existingseawalls or be situated in locations where seawalls would be naturallydesired to minimize ocean wave damage, and because it would not containany environmentally hazardous materials, would overcome manyenvironmental concerns. Furthermore, it has the potential to be used inthe open ocean as a free floating or tethered wave energy converter(WEC) array if so desired. The lack of complicated mechanical componentsand systems and the simple repetitive structure of exemplary embodimentswould allow the present principles to principles to address manyproblems associated with known systems.

For example, certain ocean linear electrical generator (LEG) deviceshave been characterized by low efficiency magnetic flux field coillinkage, heavy magnetic metal armatures, complicated mechanicallinkages, insufficient rotor stroke or range of motion making them veryinefficient in handling anything but the smallest waves, usage in singledevices or in widely spaced arrays making the efficiency in extractingelectrical energy over a given area of ocean extremely low, usage ofmechanical impact breaking systems to limit stroke range, such as duringa storm, with short life spans and severe energy wastage, low ocean waveenergy capture and dissipation capacity leading to low electrical poweroutput, significant electrical eddy current losses within the device,poorly designed coils, exceedingly powerful rare earth magnets in hugesizes that were astronomical in cost and dangerous to use, preciseoperational requirements including steering into wave fronts, lack ofability to cope with the twisting and bending forces that are presentalong with the significant vertical wave motion causing mechanicalstress and failure, excessive flux leakage, and inefficient magneticpole placement. While some systems employ the concept that the magnetsof a LEG and the field coils of that generator in an WEC should be inseparate water tight containers for the purposes of simplicity,reliability, cost, and achievement of a water tight seal, it is believedthat such an arrangement sacrifices some efficiency as the coil magnetgap becomes larger than necessary and sliding mechanical linkages usingbearings are required. Likewise, it is believed that the most efficientmeans of magnetic flux linkage remains an arrangement by which a fieldcoil array (FCA) encircles a permanent magnet array (PMA) and that anyadvantages of maintaining the FCA and PMA in separate containers can beachieved by having both in the same water tight container. It isbelieved that the current embodiments of the present principles overcomethe many deficiencies listed above.

Furthermore, if a seawall is made out of an arrangement of componentunits comprising wave energy converters (WEC's) in accordance with thepresent principles which in turn comprise linear electric generators(LEG's) whereby impinging wave fronts can be intercepted and theirdamaging kinetic energy dissipated and turned into useful electricalenergy as the waves went through the structure, any structure or coastline behind such an apparatus would be given some or complete protectionfrom wave damage. Unlike a conventional sea wall, the wave fronts wouldpropagate past the structure in an attenuated form. Such an apparatuscan have to have the following characteristics to allow for reasonable,practical, and commercial use:

The devices should capture a reasonable fraction of the wave energy inirregular waves in a wide range of sea states over a reasonable area ofwater.

Because there is an extremely large fluctuation of power in the waves,the peak absorption capacity should be up to 10 times larger than themean power absorbed. This ratio should be at least 4.

The device should efficiently dissipate wave motion kinetic energy andconvert it into electrical energy. Wave power is available at lowspeeds, linear in nature, and at high force with the forces of motionnot lying necessarily in a single direction. Most readily availableelectric generators operate in a rotary motion at higher speeds withreadily available turbines that require a constant, steady flow ofmoving medium.

The device should able to survive storm damage, saltwater corrosion,snapped mooring lines, snapped power transmission lines, broken welds,seized bearings. Thus, multiple moving parts is a distinct disadvantage.

The device should be as simple as possible both electrically andmechanically, and should be able to be scaled up in size significantly.

The electricity converter system, whether it is AC to DC, AC to AC, orAC to DC and back again to AC, should allow for power to be taken offfrom the device, which involves a mooring system that should bereasonable in costs to build and maintain and power collection circuitrythat efficiently accomplishes this function.

Noise pollution, chemical pollution from hydraulic fluid leakage, visualdetraction to the environment, and other ecological concerns should beavoided.

The system should be easily repairable with component parts easilyswapped in and out.

Ocean waves should be attenuated to a reasonable and significant degree.

An exemplary Electrokinetic Seawall system embodying the presentprinciples that can achieve these features is composed of an array ofwave energy converters, each of which is in turn composed of a group ofpermanent magnet arrays (PMA's) interspersed between a network of fieldcoil arrays (FCA's) to produce a matrix of Linear Energy Generators(LEG's) that absorbs and mechanically couples incident mechanicalkinetic wave energy and then dissipates it through electromagnetic meansvia the Faraday-effect producing electrical energy that can be carriedaway from the device, thereby allowing the coastline and structuresbehind the Electrokinetic Seawall, which can include a conventionalseawall to which it which it may be attached, to be sheltered fromdamaging and undesirable wave action.

An exemplary Electrokinetic Seawall device in accordance with thepresent principles includes a linear or other geometric array offloating component Wave Energy Conversion Units or WEC's that are eachattached to an adjacent conventional seawall or to each other, tethered,or otherwise attached to the seabed; the array may be freely floating aswell. The floating component units may be attached via metal chains orsprings to a variable number of adjacent units depending upon the shapeand configuration of the linear or geometric array. Depending upon itslinear or geometric shape, the array may be moored at one or both ends,at the corners or in the center to the seabed floor or an adjacentnearby conventional seawall or bulkhead. Each repeating component unit,which by itself has the capacity to simply float on or just below theocean's surface consists of 4 subunits: 1) a virtually fixed portionthat is neutrally to slightly positively buoyant and is located somewhatbelow the ocean's surface called the fixed subunit, 2) a heavilypositively buoyant mobile portion that consists of a buoy floatationcollar that floats on the ocean surface and oscillates vertically up anddown as ocean wave crests and troughs pass, called the mobile subunit,3) an inertial stabilizing unit that keeps the neutral to slightlypositive buoyant fixed portion from moving appreciably with the passageof ocean waves, and 4) an electrokinetic transducer, called a“Vibrational Energy Electrokinetic Transducer” or “Vibrational EnergyLinear Electric Generator” (VLEG) that comprises a matrix of PMA's(Permanent Magnet Arrays) surrounded by a matrix of FCA's (Field CoilArrays).

Movement of the mobile subunit relative to the fixed subunit inaccordance with an exemplary embodiment causes magnetic lines of forceemanating from the PMA's to cut through the FCA's inducing an electricalvoltage and current in the coils. Either the FCA's or the PMA's can beattached to the fixed subunit. Whichever of the two arrays is attachedto the fixed subunit, the other is attached to the mobile subunit. EachPMA is surrounded by a FCA. If the PMA moves and the FCA is fixed, thePMA is the linear rotor of a linear electric generator (LEG) and the FCAis the linear stator of the LEG. If the PMA is fixed and the FCA moves,then the PMA is the linear stator and the FCA is the linear rotor. Ineither case, one PMA and one FCA pair form an LEG and in either casethere is motion of one PMA relative to one FCA causing magnetic lines offorce from each PMA to cut across the copper wire turns of the FCAinducing a current and voltage in the FCA. Every electrical generator,whether the conventional rotary kind or the linear kind, has the powerproduction component called the armature, and hence in accordance withthe present principles, the FCA is the armature of the LEG. In eachelectrokinetic transducer subunit, to which the nomenclature,Vibrational Energy Linear Electric Generator or VLEG is assigned, thereare one to several pairs of PMA's and FCA's of given arrangements andgeometries, with the two components of each pair moving relative to eachother via a dual spring suspension system. The motion imparted to eachLEG pair is derived from the passage of an ocean wave, the kineticenergy of which is transmitted to the buoy floatation collar subunit andthen transferred to the vertically oscillating rotor by means of thedual spring suspension system that attaches each linear rotor of eachLEG to the vertically oscillating buoy floatation collar subunit and tothe virtually stationary fixed subunit on which the stationary stator ismounted. All of the linear rotors oscillate in a vertical manner inresponse to the passage of the wave crests and troughs. All of thestators can be attached to the fixed subunit by rigid means. The lengthof travel of the rotor, referred to as the stroke distance, is dependenton the geometric length of the rotor and the stator which can be variedfrom very small dimensions to large dimensions to capture the energy ofdifferent size waves or partially capture the energy of very largewaves. It can be shown that there is an optimal arrangement of thelength of the rotor to the length of the stator and that there is anoptimal mechanical resonance frequency of the dual spring suspensionsystem.

To help insure that the fixed subunit remains as immobile as possible asthe ocean waves pass through, the fixed sub-unit is attached to anInertial Liquid Wave Damping Stabilizer (ILWDS) which comprises astructure of significant mass containing a significant volume ofconfined immobilized water acting as a ballast mass to steady the fixedsubunit and prevent it from oscillating up and down in synchrony withthe mobile subunit, thereby maximizing the magnitude of the relativemotion of the mobile subunit (and hence the one or more multiple rotors)relative to the fixed subunit (and the one or more multiple fixedstators).

To the extent that electrical power and energy is produced in each pair,a certain corresponding and greater amount of kinetic energy is removedfrom the passing wave, rendering its amplitude after passage through theelectrokinetic seawall smaller which in turn renders its effects on thecoastline to be less than it otherwise would have been. In effect, acertain amount of damaging kinetic energy which would have beendissipated as damaging and useless heat and friction on the coastlinehas been converted to useful electrical energy which then may becollected and brought off the described apparatus for use as desired.The higher the induced electrical energy amount produced from a passageof a wave to the amount of kinetic energy dissipated from the passingocean wave determines the efficiency of energy conversion. If these twoamounts are equal, the conversion efficiency is 100% which of coursewould never be reached. However, proper and careful design of thepresent principles can lead to very high efficiencies of conversion,especially if a geometric array or mesh of many rows and columns of WECrepeating component units are used covering an area of ocean surface.

In accordance with one embodiment, since each WEC repeating componentunit of the electrokinetic seawall contains one VLEG matrix, eachcontaining one to several PMA and FCA pair LEG's, the total kineticenergy dissipation from incident ocean surface waves represents asummation of the contributions from many component units, eachcontaining several LEG's. The present principles provide several methodsby which this electrical energy can be collected and stored, includingthe diversion of a small amount of electrical power for the purpose ofilluminating the electrokinetic seawall so that it would always bevisible in the darkness of the night. The amount of kinetic energydissipated and the amount of electrical power produced is proportionalto the height of the electrokinetic seawall and the stroke length of theVLEG rotor which, for one row of WEC's, determines the maximal waveheights from which it can dissipate efficiently the kinetic energy; thesize of the waves incident upon the WEC's; the wave frequency; the angleof incidence (unless the ‘seawall’ is tethered and freely floating so itcan align itself with the direction of the incident waves or is of acircular geometric shape where the direction of wave propagation is nolonger an issue); the length of the seawall; how many layers of WECcomponent units are composing the seawall, with each layer or rowdissipating a portion of the kinetic energy of a wave whose energycontent would exceed the capability of energy dissipation for a singlerow or layer; and the shape of the seawall (curved, straight, closedshaped etc.). It is important to note that very large waves can behandled by a Electrokinetic Seawall comprising several layers ofcomponent units, with each layer dissipating a certain portion of thekinetic energy of the oncoming ocean wave producing in effect a similarkinetic energy dissipation effect and electric energy production equalto one layer of WEC component units with very long LEG rotor strokelengths. The efficiency of wave kinetic energy dissipation increaseswith each additional layer or row of WEC's, thereby removing a fractionof the kinetic energy of a large wave larger than that which can beaccommodated by the stroke length of a single row or layer of WEC's.

While one known system that encompasses the technology employingseparate watertight housing for the PMA and FCA with the two componentsof the LEG sliding via bearings and slide over an air gap between thetwo housings have low tolerance requirements, it is important to notethat although tolerances can indeed be built to be quite tight (forexample, the air gap spacing between the huge LCD stators and huge PMArotors in the gigantic Hoover Dam generators built in the 1930's wasonly 0.001 inch without the benefit of computerized design andassembly), costs increase dramatically if such tolerances are employed.Furthermore, one sacrifices efficiency in terms of magnetic flux leakageand air gap increase if the rotor and stator components are housed inseparate watertight compartments and allowed to slide over each other.In the system in which the PMA and FCA are in separate housings, onewould have to line the inside or the outside of the housings with sideto side PMA's and FCA's, each with its bearing slide system to obtainthe same magnetic flux confinement crossing from the PMA to the FCA whenthe PMA is completely encircled by the FCA. In the encirclementconfiguration, almost every magnetic flux line emanating from a PMA willcross the FCA windings at some point during its return path to that PMAor an adjacent PMA in accordance with designs of the present principles,which is not the case in the two-housing system. Furthermore, since theair gap has been made as small as 1/32 of an inch in prototypes of thepresent principles with much thinner gaps possible, it is difficult toproject that an air gap between the two watertight encasements of theprior art that is held to a constant level by the diameter of a seriesof bearings in a slide can result in a sliding bearing system with sucha small air gap, especially with the use of multiple LEG's locatedaround the periphery of the encasing shells. Finally, there is no needfor certain embodiments of the present principles to handle the largestwaves—first they would occur rarely, second in all probability aninternal breaking system that will be described in more detail below canbe employed to activate and shut off the device, and third, as justnoted above, multiple layers of WEC's with LEG's of shorter strokelengths can substitute the more difficult to construct single layer ofWEC's with very long stroke lengths.

To ensure the survivability of embodiments of the present invention inthe face of very rough seas several additional features can be employed.For example, an automatic shutoff mechanism can be used to prevent therotor from moving too far and too fast in rough weather characteristicof ocean storms which would otherwise damage the device. Hence,considering that impact break mechanisms to limit stroke length arehighly undesirable for previously mentioned reasons, the breakingmechanism should be electromagnetic using either shorted coils at theend of the FCA or large metal reaction plates or rings there. Further,in contrast to known systems, embodiments of the present principles canswitch out the braking coils automatically in an abrupt manner so thatpower generated in the VLEG is wasted in the braking power only duringthe passage of an excessively large wave. The rotor baking mechanism canalso rely on direct magnetic repulsion by magnets that repel the PMA ifit gets too close, and can use both the counter electromotive force(EMF) generated by the shorted coils or reaction plates as well aspurely magnetic breaking to stop the rotor and make it immobile in veryheavy seas. Yet still another component of the braking mechanism can usesprings to decelerate the rotor with an excessively large wave. Also, tofurther improve the survivability of the electrokinetic seawall, if aWEC unit in the seawall shorts out, the device can be immobilized due tothe electromagnetic breaking of the large counter EMF that will develop,and thus a shorted out WEC will not affect other WEC units or if itdevelops an open circuit, it will at first oscillate very easily asthere is no back EMF counter force but it will shortly encounter theshorted out coil of the breaking portion of the FCA as well as thestationary breaking magnet and spring and it will then stop oscillatingagain leaving the other units unaffected. If just one coil of a FCA in aWEC unit shorts out, the rotor might momentarily decelerate near theshorted coil from the large counter back EMF that will develop, but theWEC in this condition will remain functional though at a lesserefficient level. Furthermore, a power output circuit by electronic meanscan neutralize the effect of shorted out or open circuit Field CoilArrays so that they would not make the whole apparatus non-operational.The integration together of these varied techniques for brakingexcessively moving rotors and dealing with electrical shorts and opencircuits provide improvements over known systems. Furthermore, means areprovided to remotely switch off the WEC in the event of dangerousweather or electrical instability as well as monitor the status of thesystem by a remote visual monitoring method all making use of internetcommunications; known systems do not incorporate such means.

By illustration of when an Electrokinetic Seawall embodiment is placedin a body of water such as an ocean, very large lake, estuary, or bay,and it is deployed and constructed in a pattern to just simply produceelectric power, or dissipate wave kinetic energy to protect a nearbypiece of coastline, passing ocean waves apply a force to the movingsubunit of each seawall component unit which causes this moving subunitcomprising a buoyant floatation collar buoy to move up and down relativeto the fixed subunit of each seawall component comprising a neutrally orslightly positive buoyant mass whose center of mass is well below theocean surface and located at the point of a 3^(rd) subunit of theseawall component unit, the Inertial Liquid Wave Damping Stabilizer(ILWDS) that is also part of the fixed subunit. The fixed subunit may beanchored or tethered to the seabed or adjacent conventional seawall byeither flexible or rigid means or left floating. A 4^(th) subunit of theseawall component unit in this embodiment, the VLEG array composed ofPMA's encircled by FCA's, is partly connected via a pair of springs tothe mobile subunit (the rotor) and partly connected to the fixed subunit(the stator). The linear stators of the LEG's of the VLEG are attachedto a plate which is fixed to the fixed subunit and the linear rotors ofthe LEG's of the VLEG are attached to a plate which is fixed to themobile subunit. There are two functionally equivalent rotor stator pairconfigurations: either the rotor may be a PMA and the stator iscorrespondingly a FCA, or the rotor may be an FCA and the stator iscorrespondingly a PMA. In either case, relative motion is producedbetween each PMA and each FCA of each LEG in each Vibrational EnergyElectrokinetic Matrix Transducer which results in magnetic lines offorce emanating from each PMA cutting the copper coil turns of thecorresponding encircling FCA resulting in a certain quantity of kineticenergy of the passing wave being dissipated by each LEG and a certainquantity of electrical energy appears in its place. The size of theVibrational Energy Electrokinetic Matrix Transducer (VEMT), the namegiven to the structure composed of a three dimensional arrangement ofnumerous VLEGs functioning as one transducer converting kinetic oceanwave energy to electrical energy, can vary greatly in size ranging fromthe simplest—a single pair of permanent magnets whose like poles arebonded under force together surrounded by 4 field coils—the basic VLEGunit—to larger ones with many permanent magnet pairs surrounded by manyfield coils forming one LEG which in turn is surrounded by anywhere from1 to 8 other LEG's to form a matrix of field coil arrays and permanentmagnet arrays containing many magnets and coils. Size also depends onthe size of the coils and magnets themselves.

The configuration of magnetic poles of the PMA in preferred embodimentshas been given the nomenclature, Compressive Repulsion Magnetic Fieldtechnology (CRMF) that results in minimized flux leakage, maximizedmagnetic field intensity and total magnetic flux lines cutting acrossthe coil windings in the region occupied by the FCA; the quantity ofelectrical energy produced as a result of dissipation of a givenquantity of wave kinetic energy is thereby maximized increasing theefficiency of this electrokinetic transducer. In this configuration,similar magnetic poles of adjacent magnets of the PMA are forcedtogether under great force to produce these magnetic fieldcharacteristics. These magnets should be stabilized with various meansto prevent the component magnets from flying apart. The dimensions ofthe magnets of the basic VLEG electrokinetic transducer exemplaryembodiment are related in a precise way to the geometry of thesurrounding set of field coils and, to maximize the voltage produced andminimize the magnetic flux leakage away from the coils, precise rulesregarding the number of magnets in each PMA, each FCA, the orientationof the PMA of one VLEG with respect to the PMA of its neighbors and thepolarities of the terminal magnets of each PMA can be employed toaccomplish these objectives, as discussed in further detail hereinbelow. The stroke distance through which the vibrational energyelectrokinetic transducer embodiment operates can be shown to be relatedprecisely in a most favored configuration to the longitudinal axiallength of the PMA. For maximum transfer of kinetic energy from thepassing wave to the oscillating rotor, the frequency of oscillation ofthe rotor that is determined by the incoming wave frequency in the mostfavored configuration should be as close as possible to the naturalmechanical resonant frequency of the spring mass system composing therotor and its attachments in exemplary embodiments. The amount ofkinetic energy dissipated from a given wave of a given height depends bythe combined Faraday induction effect of one to many VLEG's within theVibrational Energy Electrokinetic Matrix Transducer and for each PMA-FCAVLEG pair, upon the size and magnetization strength of the rare earthmagnets composing each PMA, the size and number of turns of each coil ineach FCA, the number of magnets in each PMA, the number of coils in eachFCA, the length of the each LEG, the length of the vertical stroke ofeach LEG, the air gap between each PMA and its corresponding FCA, themaximum velocity of each rotor relative to the corresponding statorwhich is in turn dependent on for a wave of given height on the buoyancymass displaced by the mobile subunit and the mass of the rotor relativeto the mass of the fixed subunit, and finally, by the mechanicalimpedance matching that transfers the mechanical kinetic energy of thewave first to the mobile subunit, and then second sequentially to themoving linear rotors of the Vibrational Energy Electrokinetic MatrixTransducer, which in turn depend on the closeness of matching therotor's spring mass natural mechanical resonance frequency with thefrequency of the most frequently encountered incoming waves as well asoptimization of the ratio of the axial length of the PMA to the strokedistance through which the PMA oscillates. This energy transfer can beaccomplished via a stainless steel dual non-magnetic spring and flexiblecable system which, because of its high tensile strength, flexibility,and temporary potential energy storage ability, allows for extremelyefficient mechanical energy transfer and is tolerant of the twisting andbending forces produced by the small but yet significant horizontal androtational motion vectors of the ocean surface wave as it impacts andtraverses the seawall as well as its interaction with other oceansurface waves in its vicinity. All of these factors should be consideredto achieve the highest efficiency of desired wave kinetic energydissipation via conversion to electrical energy, and, in addition,magnetic flux leakage, ohmic resistive losses, hysteresis losses, Lenz'sLaw counter EMF losses, and eddy current formation losses should beminimized. All of these factors have been dealt with in preferredembodiments without the need for any hydraulic or bearing mechanicaldevices to achieve the magnetic flux linkage needed to dissipateundesirable wave kinetic energy into useful electrical power.

A Power Collection Circuitry (PCC) system in accordance with anexemplary embodiment of the present principles uses several differentnovel features that are distinctly different from and advantageous tothe known systems which generally rely on single phase or 3-phase ACelectrical power output with or without DC rectification by variousmeans. The problem of combining many sources of asynchronous AC and DCvoltages from the many power output terminals from the numerous VLEG'sof multiple WEC repeating units of the EKS is dealt with in thisinvention and solved in each of four ways described below using networksof appropriate electronic components.

Survivability in adverse conditions is important in embodiments used asa seawall. There are at least eleven important factors should beconsidered: 1) Components of the device should be non-corroding in seawater; 2) The Vibrational Energy Electrokinetic Matrix Transducer (VEMT)should be contained in a water tight container; 3) The mechanicalinterface where the kinetic energy of the ocean surface wave istransferred by the spring into the VLEG assembly should be water tight;4) The vertical stroke should be limited and the action of the LEG'sshould cease if waves of a certain size produce an excessive amount ofvertical motion in the VLEG electrokinetic matrix; 5) The seawall andits repeating WEC components each comprising the 4 previously describedsubcomponents should be able to resist the violence of severe waves; 6)The Electrokinetic Seawall should be located away from other structuresincluding conventional seawalls by a sufficient distance to preventcollision of the seawall which is flexible and may move in position inthe ocean water depending upon anchorage and tethering arrangements (ifsecurely attached to a conventional seawall by rigid means of sufficientdistance this is not a concern); 7) The repeating WEC component of theEKS should be attached to each other by such means and be sufficientlyfar from its neighbors so has not to cause collisions with each other inlarge waves. 8) The mechanical or electrical failure of a repeating WECcomponent of the EKS should not make the entire system non-functional;9) The repeating WEC component of the EKS should be serviceable andeasily replaceable keeping the rest of the system intact; 10) The EKSshould be easily visually observable by ships; 11) The remote systemshould be visually observable by remote control by system operators. Allof these factors have been considered and dealt with in embodiments ofthe present principles described herein.

FIG. 1A provides a side view of the external appearance of an exemplaryElectrokinetic Seawall (EKS) system embodiment comprising a group of arepeating WEC components. Other more specific exemplary EKS systemimplementations are illustrated in FIGS. 1B, 1C, 2A, 2B, 12A-12E(2),13A, 13C, 13D and 13F. In general, an EKS system can include a pluralityof WECs, where each of the WECs includes a buoyant portion, for example,192A, configured to be disposed above a surface of a fluid medium, theocean in this example, when the WEC is immersed in the fluid medium.Further, each of the WECs is configured to convert mechanical energy ofwaves traversing the fluid medium into an electrical current. Asdiscussed in detail herein below with respect to the various exemplaryEKS systems, the plurality of WECs are affixed such that distancesbetween adjacent WECs of the plurality of WECs are relatively close todissipate the mechanical energy of the waves over an area of the fluidmedium and thereby protect one or more structures or areas behind theEKS.

Referring to the EKS example illustrated in FIG. 1A, each Wave EnergyConverter (WEC) 191 is connected together by suitable means ofsufficient strength, semi-rigidity, and flexibility or elasticitycomprising tether or connector 6, which may be a chain, a spring, or acable made of a material not subject to corrosion such as stainlesssteel, heavy nylon, or any material commonly employed in the mooring ofstructures in the marine environment. The length, semi-rigidity andtension of the tether 6 should be such that the action of the wavesimpinging onto the EKS would not cause the WEC repeating component 191to crash into and damage its neighbor. The tether or connector 6 inother exemplary embodiments may be rigid. A minimum spacing is preferredto separate one WEC 191 from its adjacent neighbor and this minimumspacing is given by s=4L sin 60°, where s=the minimum spacing between aWEC 191 and its neighbor, L=the height of the buoy floatation unitconsisting of a buoy top structure 1 and a bottom base floatation collarstructure 2 that floats on the surface of the ocean, and 60° representsthe maximum angle of tipping from the vertical by the WEC 191 expectedfrom the largest waves impinging upon the EKS apparatus. The designshould allow for two adjacent WEC's tipping toward each othersimultaneously (2L sin 60°) with a safety factor of 2 added yielding 4Lsin 60° as the minimum spacing; designing in a safety factor of 2.309,which would protect the adjacent WEC's from collision even in the almostimpossible event that such a great wave that both adjacent WEC's wouldbe horizontal toward each other, we get s=4L designing in a tippingangle of 90° from vertical. This will maintain the proper minimumspacing between adjacent WEC's so as not to cause either their basefloatation collars 2 or their buoy tops 1 to collide into each other. Ifpossible, the preferred arrangement is to employ the 4L sin 60° spacingto maximize the benefit of ocean wave dissipation by EKS embodiments. Byadding weight to the fixed subunit and making its center of gravity asdeep as possible below the ocean surface, the stability of the WECrepeating component during the passage of large waves will be improved,as the WEC will be able to maintain a fairly erect posture with even thelargest of waves, thereby decreasing the tipping angle from the verticalconsiderably. Thus, this minimum distance between adjacent WEC's will beable to be decreased markedly. If each WEC is fixed rigidly to the seawall behind it that it is protecting, or if it is rigidly attached tothe sea floor via rigid means, this minimum inter-WEC distance goes downto a matter of inches. Also for safety considerations, each WEC is litwith a Power LED module 205 at the summit of the buoy floatation collartop so that the Electrokinetic Sea Wall can be illuminated in darknessmaking it visible to passing ships. The apparatus is moored to mooringpoint 4 on the shoreline, attached to a conventional sea wall, oranchored to the sea bed.

The WEC 191 itself comprises an upper structure designed to float on andabove the ocean surface comprising buoy floatation unit 192A formed bybuoy top 1 and floatation collar base 2 and a lower structure 193Adesigned to be neutrally or slightly positive buoyant and float at orjust below the ocean surface formed by metal top plate 5, buoyancycollar 15, an encasing metal stem shell 7, a metal heave plate 8, ametal brace 9, and a stabilizing metal water filled weight 10. The buoyfloatation unit 192A and the buoyancy collar 15 on the lower submergedstructure can be made of any of possible lightweight materials that arecustomarily used in buoys, floats, and rafts such as Styrofoam,polyurethane foam, wood, etc. The metal composing the submerged lowerstructure and its parts should be non-magnetic and relativelynon-corrodible in both salt and fresh water and can include metals suchas stainless steels, titanium, or brass; stainless steel, because ofcost factors, widespread use and availability, and corrosion resistancebeing the preferred metal.

In its deployment into a large body of water which may be an ocean, aharbor, a large lake, a bay, or estuary, the array of WEC's forming theEKS are exposed to oncoming waves. The oncoming wave lifts the upperbuoy floatation structure 192A as the crest approaches lifting itsfloatation collar base 2 vertically upwards away from top 5 of the lowerbuoyancy neutral or slightly positive structure 193A which staysrelatively fixed in position relative to the water's surface because ofits much greater mass as compared to the upper structure. When the wavecrest passes, and the water height begins to descend, gravity forces theupper structure 192A downward, which continues to descend until the wavetrough impinges upon the EKS. At that point, the upper structure 192A,still floating upon the water's surface is at its lowest height, andclosest to the top 5 of the lower submerged structure 193A. Once thetrough passes, and the water surface begins to rise toward the wave'sneutral point or node (zero point), the upper structure 192A movesvertically upward separating itself from the lower unit which continuesto be relatively stationary. The cycle repeats for each wave thatpasses.

The function of the WEC 191 is to dissipate unwanted mechanical kineticenergy of the wave as hits a seawall, a coast, a harbor, or otherstructure exposed to waves thus preventing damage or a shorter life ofthe involved structure. It converts the energy to a useful form, in thiscase, electrical energy. The mechanism by which it does this is theFaraday Linear Electric Generator.

The Faraday Effect, described by Faraday's Law, the third law ofMaxwell's equations describing all known electromagnetic phenomena,occurs when there is relative motion between a magnetic field and aconductor, usually a metal wire, immersed in that field which causes acurrent and voltage to be induced in that conductor. The movement of themagnetic field relative to the conductor may allow for either themagnetic field being stationary or the conductor being moved, or theconductor is held stationary while the magnetic field is moved. Ineither case, mechanical energy is being applied to move either theconductor or the magnetic field, and some of this mechanical energy isconverted to electrical energy consisting of the product of the voltageand current levels integrated over time induced within the conductor.Magnetic fields are composed of magnetic force lines called magneticflux that emanate from the North pole of a magnet, electromagnet, or amagnetic field set up by the motion of a charge current (Ampere'sLaw—Maxwell's fourth law) and by established convention terminate on thesouth pole. The stronger the magnet, the greater the field intensity,and the greater the density of the flux lines in the magnetic fieldproduced by that magnet. If the conductor is wound into a coil, the moreturns, and the greater the length and cross-sectional area of the coil,the more flux lines will cut across it when there is relative motion ofthe magnet with respect to the coil. Since the voltage, current, andthus the power and energy levels induced in the conductor isproportional to the amount of magnetic flux lines cutting across thecoil per unit time, the amount of mechanical kinetic energy convertedinto electrical energy by a system consisting of a magnet or magnets,and a coil or coils, the defining elements of the system known as anelectrical generator, will depend upon the velocity of the relativemotion of the magnet (s) and coil (s), the strength and size of themagnet, the medium through which these magnetic flux lines travel(magnetic material has a high permittivity that offers much greater easeto the flow of magnetic lines of force), the dimensions of the coil, thenumber of turns in the coil, the thickness of the wire forming the coil,and how well the magnetic field lines can be focused, concentrated, orotherwise directed onto the coil. The concept of the air gap is animportant factor for maximizing the amount of flux lines interceptingthe conductor. Because air is non-magnetic and offers great resistance(very low permeability approximately that of a vacuum) to the flow ofmagnetic flux lines of force (in air the density of the flux falls offwith the square of the distance between the magnetic pole source of themagnetic field and the conductor), this air gap should be kept as smallas possible.

Having described in elementary terms the theory of operation of anelectrical generator, we can now explain the functional operation of theLinear Electric Generator in EKS embodiments. Most generators arestructured so that a rotary mechanical motion caused by a unidirectionalmoving medium, such as water, steam, an engine belt, wind etc.,intersects a turbine rotating machine to rotate a bank of magnetsassembled around a circular structure at high velocity within a set ofstationary conducting coils, usually copper, surrounding the magnets. Itis also possible for the magnets to be in a ringed stationary structureenclosing a rapidly rotating structure consisting of conducting coils ofwire. The effect is the same and symmetrical for either arrangement. Themoving portion of the generator is called the rotor, and the stationaryportion is called the stator. The power is generated in the coilwindings, called the armature.

The conventional rotary generator in all its forms cannot be useddirectly, and can only be used indirectly with linear to rotary motionconverter apparatus, usually of considerable complexity, when attemptingto convert the mechanical energy of ocean waves to electrical energy.The problem with ocean wave kinetic energy is that it is not generatedby a unidirectional relatively constant and uniform flow of a mediumexerting a mechanical force vector always in one direction allowing itto turn a turbine rotary structure. Hence the value of the rotarygenerator is seriously compromised when attempting to use it for thepurpose of dissipating the kinetic energy of waves.

As already discussed, ocean waves are approximately sinusoidal verticaldisturbances, that while they propagate in a uniform single direction,virtually all of the mechanical force exerted by a wave is in thevertical direction and little in the horizontal direction. This verticalmechanical force follows a sinusoidal pattern with time, first in onelinear direction upward, and then in the other linear direction downwardfrom the ocean's surface.

The Linear Electric Generator is ideally suited for this purpose becauseit is capable of capturing the vertical oscillating wave force impingingupon it and as a result, because its rotor is a linear structure ofmoving magnets or coils, and its stator is a linear structure ofstationary coils or magnets respectively, it captures the mechanicalkinetic energy of the propagating wave with high efficiency as its rotoroscillates vertically in the same plane as the oscillation anddisplacement of the water particles constituting the wave. What resultsis a linear motion of the rotor relative to that of the stator in phasewith the oscillating force vector of the wave. The larger the wave, thegreater the mechanical force and energy impinging upon the LEG, thegreater the acceleration and velocity of the rotor in the direction inphase with the impinging wave, the more magnetic flux lines that are cutby the coils per unit time, and the more mechanical energy is dissipatedinto electrical energy, which can then be directed away through poweroutput circuitry to a load to perform useful work. It is capable ofefficiencies of up to 90% because it requires little in the way ofmoving parts other than the rotor. Because it is important that themaximum velocity of the rotor be developed relative to the stator, thestator can be fixed to a large structure, such as the seabed, or to someother large structure to keep the stator largely stationary. It isimportant also to make the rotor as massive as possible, consistent withthe limiting factor of keeping the mass of the upper mobile structure192A much smaller than the fixed submerged structure 193A, as thatallows for the largest transfer of kinetic energy to the rotor from awave containing a sufficiently high enough kinetic energy as itintercepts the WEC.

In the exemplary embodiment of the LEG used in the WEC 191, the rotor isan integral part of the upper mobile structure 192A hereon now to bereferred to as the mobile subunit, and the stator is an integral part ofthe of the fixed submerged structure 193A hereon now to be referred toas the fixed subunit. The sinusoidal variation of the distance betweenthe mobile subunit 192A containing the rotor and the fixed subunit 193Acontaining the stator as the ocean wave impinges upon the WEC 191develops the velocity of the rotor relative to that of the statorcausing dissipation of the kinetic energy of the wave and its conversionto electrical energy.

FIG. 1B depicts, looking down from above a body of water, a deploymentof an exemplary EKS apparatus 11 comprising a linear array of WEC's 11C(top view of WEC) tethered together by springs 6 and adjacent to, infront of, and tethered to a conventional seawall 147 by tether 4 therebyprotecting that seawall from wave action and damage. Together, theconventional seawall and the EKS apparatus protect the beach orcoastline 12 behind it.

FIG. 1C shows, looking down from above, a harbor seawall configurationthat resembles an actual harbor coastline 13 with 2 protected buildings122 and 123. In this configuration there are two conventional seawalls147 that shield the harbor from approaching ocean waves leaving a smallchannel 14 for shipping. In front of each conventional seawall 147 anexemplary Electrokinetic Seawall (EKS) 11 of the present principles isshowed deployed with EKS tethered attachment points 4 at the lower endof each EKS apparatus, attachment points 4 at the upper end of each EKSapparatus adjacent to the egress and ingress of the shipping lane, alinear array of attached Wave Energy Converters (WEC's) 11C (Top View ofWEC) attached by chains, springs, or cables 6. The EKS Apparatus 11provides kinetic ocean wave energy dissipation for the seawalls and bothtogether protect the harbor coastline 13 and its two buildings 122 and123.

FIG. 2A thru 2C displays top views of the interaction of the ocean wavesand waves that may be seen in large inland bodies of water with varyinggeometries of an EKS apparatus. In FIG. 2A, an EKS apparatus 11comprising two linear arrays of WEC's 11A and 11B composed of individualWEC's 11C is impinged upon by ocean waves of full intensity designatedby heavy solid black lines 16 and upon passing through the EKSapparatus, the waves are attenuated in intensity as designated bylighter broken lines 17. The protected shoreline 12 is then impingedupon by attenuated waves of less kinetic energy content and is thusprotected from erosion and other damage. FIG. 2B depicts a singleisolated WEC 11C attenuating impinging ocean wave 16 producing waves ofless intensity and smaller height 17 downstream. FIG. 2C illustrates aring configuration EKS 18 of WEC's 11C which attenuates the incomingwaves 16 of high intensity and large height to waves 17 of lesserintensity and lesser height downstream from the EKS. Note that in theseconfigurations, it is not necessary for the EKS to always be inapproximation to a conventional seawall to perform its useful functionof protecting a coastline, or dissipating kinetic ocean wave energy intouseful electrical energy. Note that any structure within the ring of EKS18 will be surrounded by relatively calm ocean and is thus protectedfrom sea wave motion. One important feature of circular or ring arraysof WEC's is that the efficiency of the EKS is not dependent uponincident wave direction of propagation and in this format the apparatusis omnidirectional without the need for steering mechanisms to maximizeenergy dissipation. For clarity, attachments between WEC's and means ofanchoring the apparatus to a fixed position are not shown.

As indicated above, an important feature of the EKS is that the WECsshould be disposed relatively close together to dissipate the energy ofpotentially damaging ocean waves and thereby protect various structureson or near a coast or even in open water. In contrast, knownarrangements of other types of vertically oscillating WEC's have usedmultiple units that were quite farther apart than the EKS embodimentsdescribed here, greatly reducing the efficiency of energy capturing fromthe propagating waves. To achieve the beneficial effects of the seawallapparatus described herein, it is believed that the spacing of the WECrepeating subcomponents should be such that the spatial distance of eachWEC from any of its nearest neighbors in any direction away from thatWEC should not be any greater than approximately 8 times the height ofone or more, preferably each, floating buoy collars, of the WECs, abovethe surface of the ocean. The basis for this distance is that any widerspacing seriously degrades the kinetic energy extraction ratio (kineticwave energy flowing into the EKS minus the kinetic wave energy flowingout of the EKS—that quantity which is then divided by the kinetic waveenergy flowing into the EKS) of the EKS array; the spacing betweenadjacent WEC's in a row perpendicular to the direction of wavepropagation will degrade this wave kinetic energy extraction, and thelarger the spacing, the greater the degradation. This degradation if notcontrolled leads to two problems—1) the amount of kinetic wave energyextracted over the area of the ocean in which the EKS is deployedbecomes too limited to incur sufficient protection of structures behindit and 2) the magnitude of the by-product of this wave kinetic energydissipation function, the production of useful electrical energy, isseriously degraded as well. This spacing problem can be overcome byincreasing the number of rows of the EKS from a linear array of one rowto the 2 dimensional geometrically variable array of many rows of themesh arrangement, described in more detail herein below. However, thismultiple row mesh configuration will only effectively make up for thespacing issue if the spacing between each WEC described above is lessthan the specified 8 times the height of the WECs above the water;spacings greater than that spacing lead to a degree of degrading of theenergy extraction ratio that the institution of a 2-dimensional multiplerow configuration may not overcome. Known arrangements of verticallyoriented WEC networks fail to take into consideration the spacingproblem and, in such configurations, the individual WEC's are spaced fartoo wide both for any meaningful wave kinetic energy attenuation, abasic purpose of the EKS embodiments, and fail to extract in a usefulway a substantial amount of electrical energy from the given area of theocean in which these networks are located.

FIG. 3A illustrates a side view of an embodiment of a WEC repeating unitof the Electrokinetic Seawall apparatus 11 at the point where a troughof an ocean wave is passing and the ocean surface is at its lowestlevel. Where not specified, all metal parts other than the PMA arecomposed of brass, stainless steel, or other non-corrodible andnon-magnetic metal, with stainless steel type 316 being preferred forsalt water marine environments, and all components made of buoyancymaterial may be composed of Styrofoam, polyurethane foam, wood, andother materials most commonly used for this purpose. The PMA in oneembodiment is preferably composed of NdFeB (NIB) rare earth magnetsalthough samarium cobalt magnets and magnets of other composition maybeused as well and pole pieces, made of hardened low carbon steel, highsilicon electric steel, or any other steel that has high magneticpermeability and high saturation properties can be used; iron is not thepreferred magnetic metal. The exemplary WEC of FIG. 3A comprises themobile subunit 19, previously described in less structural detail inFIG. 1A as structure 192A that is now drawn to approximately half scalein FIG. 3A, and a fixed subunit or stator 20 which were shown in lessstructural detail on FIG. 1A as structure 193A. The mobile subunit orbuoyant rotor 19 is configured to be driven by waves traversing a fluidmedium, which in this example is the ocean. In turn, the stator 20 isconfigured to be at least partially submerged in the fluid medium and tobe relatively stationary with respect to the rotor in response to thewaves. As discussed herein below, the WEC can be configured so that oneof the rotor or stator includes a field coil array and the other of therotor or stator includes a permanent magnetic array that is configuredto induce an electrical current in the field coil array in response torelative motion effected by the waves. In the example illustrated inFIG. 3A, the mobile subunit or buoyant rotor 19 comprises twocomponents: 1) a buoy floatation collar 26 formed by buoy floatationcollar base 2 of suitable buoyancy material such as Styrofoam,polyurethane foam, wood and others and which may be square, polygonal,or circular, the preferred embodiment, in shape; a buoy floatationcollar top 1 of suitable buoyancy material such as Styrofoam,polyurethane foam, wood and others and which may be square, polygonal,or circular, the preferred embodiment in cross sectional shape; outersliding tube 27; the upper end of fixed metal slotted rotor slidinginner tube 32, designed to be operative in the vertical and nearvertical position and its end cap 32C with hole 32B through which upperperturbing force spring 23 extends; if sliding tube 32 is made ofpolycarbonate plastic or equivalent durable plastic, the slot (not shownin FIG. 3A, but shown in FIGS. 9E and 9F) may be omitted; rubber,silicone PTFE or preferably UHMW-PE (Polyethylene) ring bumper 25;sliding waterproof sliding joint and seal 124; outer sliding tube 27 isattached to the buoy floatation collar top 1 via upper attachment point24 and buoy flotation collar base 2 via lower attachment point 24A; 2)the rotor of the VLEG 21 which in turn comprises an upper perturbingforce stainless steel spring suspension system 23; an upper and lowerspring attachment points 72 and 73 respectively; PMA 37 with centralcavity 47 of inside diameter of 0.25 inch containing stainless steeltube 36 of outside diameter of 0.24″ through which multi-strand flexiblestainless steel or mono-filament Kevlar cable 33 flows and is attachedto the upper and lower ends of the PMA 37 at attachment points 74C and39A respectively; stainless steel structural support tube 36 may also bemade of brass or any other stiff rigid non-ferrous metal material; thecable 33 attachments to PMA 37 are fixed and non-sliding so that anyvertical movement of the cable causes a corresponding equal verticalmovement of the PMA 37; a vertical stack of cylindrical rare earth NdFeBmagnets 40 composing PMA 37 that are oriented with respect to their likerepelling poles separated by interior magnetic pole pieces 35 ofelectric steel, hardened low carbon steel, or other suitable magneticmetal, end pole pieces 40A with all pole pieces being ringed bystainless steel slide bearings comprising thin stainless steel sheetbonded to interior pole pieces 35 and two end pole pieces 40A;additional stainless steel rings may be bonded to the sides of themagnets; End magnetic field deflecting magnets 212 and 213 whosethickness is a fraction of that of magnets 40 and whose pole which isattached to the end magnet 40 of the magnet stack is of the samepolarity as that of the pole at the end of magnet 40 stack and whoseother pole face is of the same polarity as the pole of braking magnets28A and 28B respectively. In the preferred arrangement, flexiblemulti-strand stainless steel or mono-filament Kevlar cable 33 ofsuitable thickness attached to upper perturbing force spring 23 atattachment point 73; cables made of other flexible high tensile strengthmaterials would also be suitable; and lower restoring force stainlesssteel spring 63 with upper attachment point 39A to PMA 37 and cable 33.All parts of metal other than the stainless steel springs 23 and 63 maybe brass, stainless steel or some other non-corrodible (in sea water)non-magnetic metal. All cable 33 attachment points may be accomplishedby knotted, epoxy bonded, cable clamped, or other suitable means.

With respect to the polarity of magnetic poles, there are threelocations within the WEC where the repelling magnetic poles of likepolarity are used in this embodiment: 1) between adjacent poles of thethick electric power producing magnets 40 of the PMA; 2) between thepole of the end magnetic field deflecting magnet 212 or 213 and the poleof the thick magnet 40 in the PMA that it faces; 3) between the pole ofeach of the end braking magnets 24A and 24B that face the end of the PMAand the respective pole of the end magnetic field deflecting magnet 212and 213 that they face respectively. It does not matter whether a southpole is repelling another south pole or a north pole is repellinganother north pole. The south pole configuration with south poles oneach of the PMA ends facing south poles of the braking magnets weregiven as one of the two possible arrangements, with a similararrangement of north poles being equivalent in structure and function.

FIGS. 3B (1) and FIG. 3B (2) depict two different embodiments of theupper perturbing force springs. The configuration of FIG. 3B (1) isstructurally similar to that what was described above with respect toFIG. 3A and the mobile subunit 1. Here, in FIG. 3B(1), cable 33 isattached to the upper perturbing force spring 23 at point 73 and to PMA37 at point 76. Two similar cables 58 are attached to spring 23 at point72 and to attachment plate 125 at point 76C via cable tension adjustmentassembly 93, a variant of a turnbuckle, a standard component used toadjust tension in spring suspension assemblies and which is made ofgalvanized or preferably stainless steel. Its purpose (not shown in FIG.3A) is to adjust the tension that should always be on the springsuspension system of the VLEG so that the natural resonant frequency ofthe system can approximately approach that of the incoming waves foroptimal kinetic energy transfer to the rotor. The configuration of FIG.3B(2) resembles the configuration of FIG. 3B(1) except that now 4additional springs 126 are added and cable tension adjustment assemblyis not shown. It is believed that the second configuration in FIG. 3B(2)incorporates additional tolerance of the WEC to torsional and rotationalforce components of the wave input force, lessening mechanical wear fromfriction on the moving rotor. Cable tension adjustment assembly 93 isalso used to adjust the tension in the spring assembly, which would tendto decrease with time, when the WEC is subject to routine maintenance.

Referring again to FIG. 3A, the fixed subunit 20 of the WEC comprises inturn four components: 1) a watertight canister or shell made ofstainless steel, brass, heavy duty polycarbonate plastic or UHMWpolyethylene plastic (with all plastic used in the present principlesbeing either of UV stabilized or UV resistant nature) or other suitablenon-corrodible in sea water non-magnetic material which in turncomprises large cylindrical tube 29; fixed subunit top 5 centrallyperforated by ¼ inch hole 64 through which cable 33 extends whosepreferred geometry is circular but may also be square, rectangular, orof other geometric shape; shock absorbing rubber, PTFE (Teflon™),silicone, or preferably UHWM Polyethylene (UHWM-PE) bumper 5A on theupper surface of fixed subunit top 5; and the upper surface of uppermetal heave plate with skirt 8; 2) the Inertial Liquid Wave DampeningStabilizer 22 (ILWDS) composed of two metal heave plates 8 of anydesired geometric shape but rectangular in the preferred configurationwith metal skirts along the entire outside perimeter of each heave platebraced together by metal brace 9 whose length is adjusted together witha suitable height of each metal skirt such that there is very littlespacing between the two adjacent upper and lower skirts resulting in avery large quantity of water essentially trapped in the cavitiesenclosed by the heave plates; a water filled enclosed metal cavitycomprising a water filled stabilizing weight or reaction mass 10 with awater ingress hole 41 on each side and an air intake and outlet hole 199connected to rubber or plastic tube 200 feeding a one way air valve 201to which a rubber or plastic hose 202 is attached; the structure isnamed as such because the water filled mass and the two metal heaveplates with skirts entrap a large volume of liquid, ocean water, andforms it into a relatively stable mass dampening the motion of the fixedsubunit caused by the waves above it; the structures of the ILWDS 22 maybe of rectangular, circular, or other geometric shape that would tend toreduce undesirable heaving, swaying, surging, pitching, yawing, androlling of the fixed subunit 20; 3) buoyancy blocks, tubes or rings 30made of Styrofoam, polyurethane foam or some other suitable buoyancymaterial, with a preferred arrangement comprising hollow tubes of Lexan™(polycarbonate plastic) of varying diameter and length consistent withsuitable and desired total buoyant force and whose interior is filledwith polyurethane foam; 4) the stator of the VLEG comprising FCA 34,which envelops the PMA 37; central slotted rotor sliding tube 32 whoseinner surface upon which the PMA 37 will intermittently slide over airgap 61 (shown in FIG. 6) is suitably lubricated and whose length in thepreferred configuration is sufficient to allow the rotor to vibratethrough a stroke length of at least three times the longitudinal axis ofPMA 37, the stroke length which is also approximately but notnecessarily precisely equal to the sum of maximum significant waveheight likely to be most commonly encountered plus an additional lengthto allow for the braking of the magnet, the presence of theelectromagnetic mechanical rotor breaking system at each end of therotor sliding tube, and fixation of the slotted sliding tube to thefixed subunit at its top and bottom; end breaking coils 31A and 31B; endbreaking magnets 28A and 28B with central inside channel 59A and 64respectively both of 0.25 inches in diameter; and water sensor switch64A. Note that with the exception of inner core holes 47, 59A, and 64,and inner stainless steel tube 36, dimensions on the WEC structure werenot listed because the WEC can be scaled down considerably to deal withsmall waves or scaled up enormously to deal with larger waves; for verylarge WEC structures, inner core holes 47, 59A and 64 can likewise bescaled up. Prototypes constructed used magnets 2 inches diameter, 1 inchin thickness and magnetization strengths of N42. One novel feature thatwill be described subsequently (FIG. 12 D, FIGS. 12 E (1) and (2)) isthat the fixed subunit can be braced to the fixed subunit of adjacentsubunits of nearby WEC's to greatly enhance its stabilizing function tobe described below.

Before further discussing the functioning and operation of embodimentsof the present principles and its components, several terms need to bedefined. First, by convention in this description, the vertical upwarddirection of motion, velocity vector, and acceleration vector is apositive quantity; the downward vertical direction is a negativequantity. Next, there are perturbing and restoring forces acting uponthe systems described herein. Perturbing forces on the WEC areconsidered to be the following: the force applied to the WEC by the wavewhich may be positive (upward) or negative (downward), and, with a puresingle wave, sinusoidal in pattern with respect to time, but with actualocean waves that are summation waves of other waves, approximatelysinusoidal in pattern; the upper perturbing force of the spring of therotor which always, because it is an extension spring, will exert aforce upward that varies from zero to a maximum in a sinusoidal fashionwith time and whose magnitude depends on its spring constant and theamplitude of the wave; and a baseline buoyancy force that is alwaysconstant, upward (positive), and determined by the geometry of the WEC.Restorative forces on the WEC are considered to be the following:Gravitational force which always acts downward on the WEC and remainsconstant; the restorative force of the spring of the stator whichalways, because it is an extension spring, will exert a force downward(negative) that varies from zero to a maximum in sinusoidal fashion withtime and whose maximum magnitude depends upon its spring constant andthe amplitude of the wave. Other forces on the WEC include the Lenz'sLaw Counter EMF force whose direction is always opposite to thedirection of the velocity vector of the rotor and frictional forces ofthe rotor against the slotted sliding tube of the stator which also isin opposition to the direction of the velocity vector of the rotor.Finally additional forces acting on the WEC as a whole consists ofmotion forces in the six degrees of freedom including heaving, swaying,surging, pitching, yawing, and rolling and are due to the complexity andless than total uniformity of the waveforms that impinge upon the WECboth in terms of structural formation and direction of propagation. Itis of a desired state, for the purpose of decreasing frictional forcesof the sliding rotor against the stationary stator and minimizing thequantity known as parasitic damping to both increase the efficiency ofkinetic energy conversion to electrical energy and decrease thefrictional wear on the components of the VLEG of the WEC, to have thesesix motion forces produce as little motion as possible in the statorfixed subunit of the WEC; this desired state is accomplished by makingthe mass of the ILWDS as massive as possible. Furthermore, it is thedesired state to minimize for the same reasons described for thestationary stator these 6 forces on the rotor and this desired state isaccomplished in this embodiment by the resistance of the springs towhich the rotor is attached to these described forces.

When the trough of an ocean surface wave containing kinetic energy ofthe motion of the wave impinges upon the EKS apparatus 11 (FIG. 1B andFIG. 1C) and its repeating component WEC 191 (FIG. 1A), the ocean watersurface level is at its minimum level. Referring again to FIG. 3Ashowing the WEC 191 in its lowest position at the wave trough, at thispoint the upper end of slotted rotor sliding tube 32 which surrounds theupper perturbing force spring 23 is up against the under surface of buoyfloatation collar top 1, buoy floatation collar base 2 of WEC mobilesubunit 19 is resting against fixed subunit top 5; outer slide tube 27is at its lowest position and watertight sliding seal and joint 124 isat its lowest position. Note that the watertight condition keeping waterout of the VLEG is maintained by the watertight sliding seal 124,hydrophobic lubrication with the preferred agent being a lubricant thatcontains polytetrafluorethelyne (PTFE) as one of its components betweenouter slide tube 27 and the slotted rotor sliding tube 32 whose upperend is contained within outer sliding tube 27, and by rubber or siliconebumper ring 25 contained within the sliding channel between tubes 27 and32. Bumper ring 25 essentially functions as an o-ring. An alternativeequally effective configuration, as shown in FIG. 3C, comprises eitherseparate O rings 215 composed of silicone, rubber, or in the preferredconfiguration, PFTE (Teflon™) or UHMW Polyethylene (UHMW-PE) as well asnon-corrodible metal brass or stainless steel piston rings in a group ofone or more that can be attached to the outer surface of the upper endof rotor sliding tube 27 in the location occupied by bumper ring 25 andin place of this bumper ring to accomplish the same purpose of awatertight shock absorber to the moving outer sliding tube 27 as itcomes to rest in its lowest position during the passage of the wavetrough. Note that watertight seal 124 may comprise a rubber, silicone,PFTE, the preferred material, or pliable foam of similar suitablesubstance in the form of a narrow collar or O ring type of structurepermeated with or coated with the suitable, preferable, but notexclusive, hydrophobic PTFE based lubricant just described. FIG. 3C alsodisplays spring cable tension adjustment turnbuckle assembly 93 that wasnot shown in the WEC diagram of FIG. 3A.

The wave crest now begins to travel away from the WEC and the oceanwater level begins to rise as the wave begins to enter its positiveslope half cycle between the trough and succeeding crest, and duringthis period of time, the sum of the force upward of the wave plus theforce upward by the perturbing force spring of the rotor plus thebuoyancy force upward on the mobile subunit exceeds the sum ofrestorative force of gravity, the restorative force spring attached tothe stator, and the opposing back EMF force all acting downward.Referring again to FIG. 3A, a buoyancy force is produced against thebase 2 of the mobile subunit 19 causing the entire floatation buoycollar structure 26 comprising base 2 and top 1 to move verticallyupward. This force, because the base 2 floats on the water rather thanbeing mostly submerged as in the case of the fixed subunit, isproportional to the area of the floatation collar base 2 floating uponthe water. Base 2 always floats on and just below the surface of thewater where the maximum wave energy flux is located. In the preferredarrangement, the cross-sectional area of the buoy floatation collar base2 should be as large as possible relative to the cross-sectional area ofthe fixed subunit 20 and be submerged for several inches beneath theocean surface where the maximum wave kinetic energy and force occurs butnot be so large as to encompass to successive wave crestssimultaneously. As buoy floatation collar base 2 and top 1 rises withthe rising water level separating the mobile subunit 19 from the fixedsubunit 20, because top 1 and base 2 are attached to outer sliding tube27 at points 24 and 24A respectively, watertight sliding seal 124 andouter slide tube 27 also begin rising; upper perturbing force extensionspring 23 begins to contract and lower restoring force extension spring63 begins to extend. A buoyancy force is also experienced by the fixedsubunit 20 but its effect is negligible and secondary to four factors—1)its mass is drastically greater as opposed to the mass of the subunit 19with this mass being in the form of a reaction mass comprised of theILWDS 22 whose center of mass is located relatively deeply below thesurface of the ocean. 2) The ratio of the buoyancy collar'scross-section surface area of the fixed subunit 20 lying at significantwater depth to that of the much greater buoyancy cross-section area ofthe mobile subunit at and just below the ocean surface causes the fixedsubunit to experience a relatively very little fraction of the waveenergy flux above it. Thus, the fixed subunit 20 moves a very smallfraction of the distance and speed of the mobile subunit 19.Furthermore, the buoyancy force on the fixed subunit, proportional tothe volume of the buoyancy ring on the fixed subunit that is completelyimmersed in the water, is designed to be much smaller than the buoyancyforce on the mobile subunit, an amount sufficient only to keep the fixedsubunit neutrally to slightly positively buoyant and prevent it fromsinking. Note that buoyancy of the fixed subunit is preferentiallyslightly positive where possible to keep its upper end in proximity tothe ocean surface; if it was precisely neutrally buoyant, then that initself could contribute to some instability and some tendency to riseand fall with the wave passage. 3) The vertical displacement and speedof vertical displacement of the fixed subunit 20 is kept much smallerthan with the mobile subunit 19 because the position of the center ofmass and gravity is located in the bottom of the WEC in the ILWDS andresides sufficiently deeply under the ocean's surface so that both thevertical component and the much smaller and less important horizontalcomponent of the water particle wave motion is much reduced at thatlocation as compared to at the ocean surface because of the drop off ofsuch motion varies inversely with the square of the depth, resulting inthe center of mass and gravity moving with the wave action above it to amuch less extent. 4) The cross-sectional area of the buoy floatationcollar that is exposed to maximum wave energy flux and force justbeneath the surface is much greater than the cross-sectional area of theupper end of the fixed subunit buoyancy foam collar 30. The result ofthe mass difference and buoyancy force difference between the mobilesubunit 19 and fixed subunit 20 causes the two subunits to separate fromeach other in the vertical distance with the fixed subunit stayingrelatively stationary and the mobile subunit rapidly rising producing arelative velocity between the two subunits. The relative velocitybetween the two subunits is transferred to the rotor by means of themulti-strand flexible stainless steel or mono-filament Kevlar cablewhich now moves with a relative velocity to the fixed subunit. Finally,the ratio of the mass of the rotor of the VLEG to the mass of thefloatation collar should be kept as high as possible for maximum wavekinetic energy transfer to the rotor, but not so high as to make themass of the mobile subunit 19 of which it is a part too high relative tothe mass of the fixed subunit 20, which would decrease the relativevelocity and distance traveled by the rotor relative to the stator onthe fixed subunit 20, thereby reducing the efficiency of conversion toelectric energy by the WEC repeating component of the EKS.

It can be shown that the force on any buoyant body subjected to incidentwave motion can be given by and is proportional to the product of thevolume of water displaced by that object, the density of water, thegravitational acceleration, g, 9.8 m/s², and the sin (ωt), with theconstant (denoted δ, the depth constant) of proportionality decreasingas the water depth increases; ω is the angular frequency of the wave.Hence the more shallow a submerged object is submerged, the more forcefrom a wave is experienced by the object in the same manner that asubmarine hardly feels the effect of huge hurricane waves if it is deepenough below the surface. It can also be shown from this relationshipthat this wave force is thus dependent upon the product of thecross-sectional area of the object exposed to the surface beingtransited by the waves and the depth to which the object is submerged asit floats on the water, that is, the volume of the water displaced bythe submerged object. Hence, one wishes the cross-sectional area of thebuoy flotation collar of the mobile subunit to be as large as possible(but less than the wave length of the ocean wave—very large ships arestationary in the water while boats whose size is less than a wavelength will vibrate considerably in the water due to wave passage—andthe overall density of the mobile subunit across the volume of space itoccupies should be as small as possible so that it will be submerged tothe least extent possible causing the force on it, and its magnitude ofvibration to be huge compared to the fixed subunit with its much higherdensity, much heavier center of mass and gravity, much deeper depth ofsubmergence at which the center of mass and gravity are located, causingthe proportional constant of the impinging force to be much lower, and amuch smaller cross-sectional area presented to the impinging wavemotion. Thus, for a given wave size, the wave force in on the mobilesubunit is a much greater force acting on a much smaller mass than themuch smaller force acting on the much greater mass of the fixed subunit.Hence, the mobile subunit oscillates over a large linear motion equal tothat of twice the amplitude of the wave, and the fixed subunit hardlyoscillates at all, creating the relative motion between the rotor andthe stator of the WEC repeating subcomponent that is important to thepresent principles.

Referring to FIG. 3A and FIG. 8D, initially as described above, the WECis in position as shown with the rotor shown by PMA 37 in the lowestposition at the point the wave trough 69 passes through. FIG. 8A shows adisplacement vs. time graph of the impinging wave. Perturbing forcerotor spring 23A is in the maximally extended position and it is storinga maximum of potential energy. Restoring force rotor spring 63C isminimally distended and is storing a minimum of potential energy. Atthis point, the gravitational force acting on the weight belonging tothe mobile subunit 19 is exactly balanced by the buoyancy force actingon it; hence it is transiently stationary. When the trough 69 passesthrough, because the rotor containing the Permanent Magnet Array (PMA)37 of the VLEG 21 is part of the mobile subunit 19, and the statorcontaining the Field Coil Array 34 is part of the fixed subunit 20, asthe mobile subunit 19 begins to move upward, it pulls up on the upperperturbing force spring 23A that is now distended and it begins tocontract; both upward forces now being exerted on the rotor PMA 37causes it to start sliding upward in the slotted rotor slide tube 32 onthe bearing surface formed from the thin stainless steel rings 38 thatsurround the pole pieces and or the magnets; the stainless steel rings38 are lubricated to prevent unwanted frictional heat energy losses andfrictional damage to the rare earth magnets or the sliding tube overtime. The relative velocity of the mobile subunit 19 relative to thefixed subunit 20 due to the displacement upwards of the mobile subunit19 produces a relative velocity between the rotor PMA 37 moving up andthe relatively stationary stator FCA 34 which causes the magnetic linesof force emanating from this arrangement of like polarity magnetic polesrepelling each other, to be described in great detail later, toefficiently cut through the FCA 34 copper coils producing a current andvoltage in these windings. The electrical energy produced in these coilsis subtracted from the kinetic energy developed by the upward verticallymoving rotor, and since that kinetic energy was originally sourced fromthe wave moving through the WEC, the kinetic energy of that wave isdecreased by at least that amount of energy that is dissipated by theVLEG in the WEC. In practice, because the WEC is not 100% efficient, theenergy dissipated from the wave exceeds that of the electrical energyproduced in the FCA during the velocity stroke of the rotor. At alltimes some of the kinetic energy of the wave is stored in either theperturbing force spring 23A or the restoring force spring 63C or bothand then subsequently released back as kinetic energy of the rotor. Notethat during this upward rising positive slope phase of the wave 67, thebuoyancy force on the mobile subunit 19 plus the upward force of thewave itself plus the contraction of the distended perturbing forcespring 23A exceeds the gravitational force downward on the mobilesubunit 19 plus the back EMF force on the rotor acting downwardproducing a net upward displacement, velocity, and acceleration.Frictional forces opposing the rotor's motion may be disregarded becauseof the lubricated exceptionally smooth bearing surfaces of the stainlesssteel pole and magnet stainless steel sliding rings. If made ofstainless steel, electropolishing the inner surface of the slottedsliding tube reduces frictional forces even further.

As the wave continues to propagate through the WEC, the rotor PMA 37moves with higher velocity with a positive acceleration as the buoyancyforce of the wave increases, reaching a maximum. The upper perturbingforce spring 23 is contracting, releasing its stored potential energy askinetic energy to the rotor while lower restoring force spring 63 isextending, increasing its stored potential energy. At the first zeropoint 68 on FIG. 8A of the wave, the status of the WEC is represented byFIG. 8C; the rotor PMA 37 and mobile subunit 19 is moving at maximumvelocity relative to the stator and fixed subunit 20, and the amount ofmagnetic flux lines being cut by the rotor's PMA 37 movement through theFCA 34 of the stator per unit time is at a maximum. At this point thevoltage and current, and hence electrical power and energy beinggenerated by the VLEG 21, is at its maximum. At this point, both theperturbing force rotor spring 23B and the restoring force stator spring63B are in less distended positions and they have a minimum amount ofenergy stored within both of them together. Also at this point, outerslide tube 27 has slid upward halfway up its sliding path (equal to therotor stroke distance which in turn is equal to the maximum wave heightthat the WEC has been designed to handle, or less for waves of smallermagnitude). Buoy floatation collar top 1 has lifted away from the end ofslotted rotor sliding tube 32.

In FIG. 8B the crest 70 of the wave begins to approach the WEC of theEKS. The velocity of the rotor PMA 37 in rotor slide tube 32 and themobile subunit 19 is decreasing relative to the stator FCA 34 and thefixed subunit 19. The amount of kinetic energy being dissipated from thewave and the amount of electric power and energy created is decreasing,and the amount of energy stored in the upper perturbing force rotorspring 23C is decreasing approaching a minimum as the distention of therestoring force spring 63A of the stator begins to increase therebyincreasing the energy stored by that spring toward its maximum amount.The rotor PMA 37 is approaching its maximum upward displacement as itslows down relative to the stator FCA 34. At this point, the sum of thebuoyancy force plus the upward wave force is still greater than theforce of gravity and the decreasing Lenz's Law back EMF force downward,and thus the rotor and the mobile subunit 19 is still moving upwardalbeit by a smaller velocity.

Referring to FIG. 8A, when the wave crest 70 has approached, the upwardforce of the wave has dropped to zero, and once again the gravitationalforce on the PMA rotor 37 and mobile subunit is exactly balanced by thebuoyancy force on it, and again the rotor PMA 37 and mobile subunit 19is at rest relative to the fixed subunit 20 and the FCA stator 34. Atthis time, there are no magnetic lines of flux cutting the coils, thekinetic energy of the wave being dissipated is zero, and the electricalpower and energy generated is zero. The back EMF force is likewise zero.The perturbing force spring of the rotor 23C is minimally distended, andthe restoring force spring of the stator 63A is maximally distended withits stored potential energy being at a maximum. Outer sliding tube 27has slid upward on watertight sliding seal 124 to its maximally elevatedposition and seal 124 is abutting up against the blocking rubber bumperring 25 attached to the upper end of the slotted rotor sliding tubepreventing the buoy floatation collar from lifting off completely fromthe fixed subunit by waves that exceed in height the design capabilitiesof the WEC; waves of a lesser height will cause the maximum heightreached by outer sliding tube 27 and watertight sliding seal 124 to riseto a lesser amount than the maximum height.

Once wave crest 70 passes in FIG. 8B, the wave enters its half cycle 71in which its slope is negative until the next trough is reached. Duringthis half cycle, the sum of the gravitational force downward on therotor PMA 37 and the mobile subunit 19, the restorative force downwardof the distended restorative force spring 63A of the stator, and theforce exerted by the wave which is now in the downward direction allexceed the sum of the upward force of buoyancy on the mobile subunit andthe rotor, the force upward exerted by the perturbing force spring 63 ofthe rotor PMA 37, and the Counter EMF force acting upward opposing therotor's motion. This net summation of forces on the rotor causes it tomove downward in increasing velocity following the negative mirror imageof the motion of the rotor PMA 37 and the mobile subunit 19 on thepositive slope half of the wave when the sum of the buoyancy forceupward, the wave force upward, and the perturbing force spring 23A ofthe rotor exerting its force upward exceeded the sum of the downwardgravitational force on the rotor and mobile subunit 19, the downwardforce exerted by the restorative force spring of the stator and thedownward directed back EMF force on the rotor PMA 37. The cycle iscompleted during this half cycle when the next wave trough approaches,and while the kinetic energy dissipated during this negative slope halfcycle is similar to that of dissipated during the positive slope halfcycle 67, the electrical power and energy generated is of oppositepolarity. During the negative sloped half cycle of the wave, the buoyfloatation collar base 2 and top 1 of mobile subunit 19 begin fallingwith the falling ocean surface, which causes outer slide tube 27 andwatertight slide seal 124 to fall, mobile subunit 19 approaches onceagain the top of fixed subunit 20, upper perturbing force spring 23steadily extends storing potential energy from the wave, and lowerperturbing force spring 63 begins contracting releasing its storedpotential energy to the rotor. When the next wave trough arrives, theoperational cycle of the WEC and the VLEG contained within it has beencompleted. At the point the trough arrives, the buoy floatation collartop 1 and base 2 settles onto the top 5 of the fixed subunit and shockabsorber 5A, with the mechanical shock absorbing effect of shockabsorber 5A on the top surface of subunit top 5 as well as the upper endof bumper ring 25 impinging on the under surface of buoy floatationcollar top 1 slowing outer sliding tube 27 and sliding watertight sealand joint 124 to a gentle stop. Note that waves smaller than the wavesof maximum amplitude for which the particular WEC was designed wouldcause the buoy floatation collar to approach but not touch bumper ring25 and shock absorbing bumper 5A at the crest and trough of the waverespectively. Furthermore, because of the electromagnetic mechanicalbraking system at each end of the rotor slide tube, waves larger thanthat for which the WEC was designed will cause the rotor to brake,thereby causing the impact of the buoy floatation collar on bumper ring25 at the crest of the wave and shock absorbing bumper 5A at the troughof the wave to be gentle in nature in consequence of the presentembodiment having been designed so that the position of the breakingmechanism at each end of the rotor slide tube is such that they initiateand perform their function at approximately the same time the buoyfloatation collar reaches structures 25 and 5A.

The slot of slotted rotor sliding tube 32 is not shown in side viewsFIG. 3A, FIG. 7A, B but is shown in VLEG cross section views in FIGS. 9Eand 9 F and is made of stainless steel, durable hard plastic such aspolycarbonate (Lexan®) or UHMW polyethylene, brass, or other sturdynon-ferromagnetic material and performs the following functions: 1)Prevents eddy current losses in the metal non-magnetic slide tube, andthus may be omitted if non-conductive plastic is used; 2) By being ableto vary slightly the inner diameter of the sliding tube by flexing theedges of the slot closer together or further apart, the slot allows fortight and exact adjustment and minimization of the air gap distancebetween the outer cylindrical magnet surface of the PMA and the innersliding tube surface; 3) Helps along with the central canal of the PMAto equalize air pressure above and below the sliding rotor preventingundesirable air resistance to the rotor's sliding velocity; if a plastictube without a slot is used, air vents 214 at either end of the tubethat is not blocked by FCA windings would be desirable for this purpose.

The preferred arrangement is to have the FCA 34 three times as long inlength as the PMA 37 for two important reasons: 1) so as to insure thatevery magnet of the PMA 37 is underneath a coil of the FCA 34 at alltimes; not doing so would waste intensely magnetic field lines of fluxthat would escape out to space seriously degrading efficiency because ofsome magnets not being encircled by coil windings; in this arrangement,virtually all of the magnetic flux lines emanating from and flowing tothe PMA 37 will intersect FCA 34 at some point and induce a voltage.While it is also a feasible situation to have the PMA 37 twice as longas the FCA 34 especially if the FCA was the rotor and the PMA was thestator, again there is severe leakage of flux lines because at any giventime many magnets would not be encircled by coil windings, plus the factthat very large PMA's are harder to work with in terms of personnel,assembly, and cost, and it is more efficient, safe, and cheaper toenlarge the FCA length; it is more cost effective to waste copperwindings over empty space than to waste large and expensive rare earthmagnets by having them not encircled by copper windings. Very long PMA'swould also be more difficult to use as a rotor as compared to shorterones or to FCA's being used as a rotor as the difficulty and safetyworking with and assembling the extremely powerful rare earth magnetsused as well as dealing with the increased lateral magnetic attractionof ferromagnetic debris along the sides of the PMA which would seriouslydegrade rotor sliding performance would become progressivelyproblematical as PMA length is increased to longer lengths. 2) It can bemathematically shown that the maximum kinetic energy transferred to anddeveloped in the rotor is related to the maximal velocity developed inthe rotor squared if the stroke length of the rotor is three times thatof the axial longitudinal length of the rotor.

While both embodiments of the VLEG are functionally equivalent, thepreferred embodiment is for the rotor being the PMA and the FCA beingthe stator for two important reasons: 1) It can be shown mathematicallythat the kinetic energy transferred and developed in the rotor isproportional to the mass of the rotor. Thus, the mass of the rotorshould be made as large as possible consistent with the ratio of themass of the mobile submit to the fixed subunit being as small aspossible. 2) There are many wire connections that are made between themany coils and the power collection circuitry (PCC). To connect manymoving coils with moving wires to a fixed positioned PCC (even allowingfor the fact that some of the PCC could be fixed to the FCA rotoritself) would produce serious reliability problems from wire and metalvibrational fatigue and eventual breakage in the rugged environment ofthe ocean. However, in certain circumstances the second embodiment witha stationary PMA and moving FCA may be the preferred structure.

Also, with the preferred arrangement, to ensure that a given amount ofkinetic energy imparted to the rotor is efficiently converted toelectrical energy, there should be two coils in the FCA for every magnetin the PMA or 4 coils for every magnet pair, and the combined width ofthese four coils should equal approximately the length of two magnetthicknesses plus two pole pieces to ensure that a coil would not be oversignificant amounts of S and N directed magnetic field linessimultaneously which would seriously degrade efficiency and power outputexcept briefly when a given coil would be over the precise center of amagnet's longitudinal thickness. If the thickness of the power producingmagnet is T_(m) and the thickness of the pole piece is T_(p), then thewidth of each of the four coils should be, in the preferredconfiguration, approximately (T_(m)+T_(p))/2. This preferredconfiguration is most efficacious when the amplitudes of the incomingwaves are relatively small, as is with case in calmer areas of theocean, or in bays, estuaries, or large lakes where the wave kineticdamage factor to structures impinged upon by the waves is less damaging.However, while this preferential configuration is used repeatedlythroughout the description of the present principles, the relationshipbetween the total number of coils of the FCA and the total number ofmagnets in the PMA can be influenced by the size of the magnitude of theimpinging waves. For smaller waves, the ratio of the number of coils inthe FCA to the number of magnets are such that the preferredconfiguration leads to a FCA whose length approximates that of the PMAand there are two coils for each magnet and 4 coils for each magnetpair. When the waves are significantly higher with significantly higherdamaging potential to structures and coastline impinged upon by suchwaves, there are two other conditions that should be satisfied for thedesired efficient functioning of the VLEG in the WEC repeatingsubcomponent of the EKS: 1) Condition 1: the magnets must, in thisexample, always be under coils of the armature during the entire time ofthe wave cycle for an anticipated significant wave height, thusresulting in an armature length of twice that of the length of the PMAand in at least twice the total number of coils in the armature as thenumber of coils that would encompass the PMA at any given time, that is,four coils per magnet and eight coils per magnet pair to preventinefficiency in kinetic energy to electrical energy power conversionbecause of excessive leakage of magnetic flux due to uncovered PMAmagnets not within coils; and 2) Condition 2: For a given amount ofavailable wave kinetic energy from a wave of given size, as stated aboveit can be shown that the maximum kinetic energy is transferred to therotor when the length of the rotor stroke distance is three times thelength of the rotor PMA, requiring in this example additional coils inthe FCA armature so that the rotor PMA will always be encompassed bycoils during this greater distance of vibration than in the distance ofvibration of the first condition. Thus there are 6 coils of width justdescribed for each magnet (12 coils per magnet pair) in the PMA when thePMA is the rotor as per the first embodiment. Given these two conditionsacting together with the preferred arrangement of 4 coils of width(T_(m)+T_(p))/2 per pair of magnets and pole pieces, there should be arange of two to six coils of the specified width per magnet, and four to12 coils per magnet pair, with the latter number of 12 coils per magnetpair and 6 coils per magnet being the most efficacious as far as kineticenergy transfer and conversion to electric energy in WEC's exposed tolarger waves; at a minimum for the larger waves there should always beat least four such coils of the specified preferential width over eachpair of magnets and their associated pole pieces at any given timeduring the ocean wave cycle requiring in this example a minimum of 4coils in the armature per magnet and 8 coils in the armature per magnetpair. An armature FCA satisfying the second condition above will alwayssatisfy the first condition above more optimally because of the greaternumber of coils yet further reducing magnetic leakage. If the width ofeach coil is approximately (T_(m)+T_(p))/2, then at any given time 4coils will be over each magnet pair with each coil intersecting magneticlines of flux traveling in the same direction (except for transientperiods of time during the wave cycle where two of the four coils wouldintersect a low number of oppositely flowing lines of magnetic flux whenthose two coils were over the precise center of a magnet in between itsnorth and south pole in the region of lowest magnetic field density)allowing for the maximum conversion of kinetic energy at a given rotorvelocity into electrical energy. For waves of smaller amplitude incalmer bodies of water, conditions one and two give way to the preferredconfiguration of 2 coils per magnet and 4 coils per magnet pair of width(T_(m)+T_(p))/2 as described previously.

Obviously, condition 2 as compared to condition 1 operative for largerwaves would be expected to produce less induced electrical power per FCAcoil and total amount of copper used in the windings is increased for aPMA of given length, decreasing the efficiency of the FCA, although thePMA operates at higher efficiency in terms of the amount of wave kineticenergy dissipated per magnet in the PMA because more kinetic energy isimparted to the rotor when the PMA length is one third that of thesignificant wave height in condition 2 as compared to when the PMAlength is one half of that of the significant wave height incondition 1. Copper coil efficiency is maximized and the quantity ofcopper used in the windings is minimized in the preferred condition,preserving PMA efficiency but only with smaller waves. PMA efficiency ofenergy converted per magnet has precedence over FCA efficiency of energyconverted per coil. Furthermore, a magnet not contained within a coil atall times is more detrimental to the efficiency of the VLEG as comparedto a coil not enclosing a magnet during some part of the wave cycle.Kinetic energy imparted to the rotor is most advantageous to theoperation of the VLEG and the present principles when this kineticenergy quantity is maximized. This is most effectively accomplished fora wave of given energy by linearly decreasing the mass of the rotor sothat the velocity is increased as a squared function. Given that thekinetic energy dissipated by the rotor and hence the electrical powergenerated, which is proportional to the kinetic energy imparted to therotor and is maximized for large waves when the length of the rotorelement is one third that of the significant wave height and rotorstroke distance, smaller more intensely magnetized magnets will cause agreater rotor velocity to be developed, thereby producing the greaterwave kinetic energy dissipation through increase magnetic flux linkagesintersected per second. While a smaller mass of the rotor does decreasethe kinetic energy transferred to the rotor for a given wave and waveforce in, because K=mv²/2, smaller, lighter, more intensely magnetizedmagnets result in a higher velocity as a more important factor as longas the total magnetic flux produced by these magnets remain a constant.

The problem of the decrease in efficiency of electrical conversion perFCA coil due to the underused coils that exist at any point of the wavecycle is unavoidable and can only be minimized unless one wishes toincrease utilization of the coils at the expense of causing some magnetsin the PMA to be underutilized such as what might occur in the secondembodiment of the present principles where a long PMA stator is utilizedwith a short FCA rotor causing a coil to always be over a magnet butsome magnets often not being under a coil. This impact to coilefficiency is secondary in importance to the decrease in efficiency ofenergy conversion that would occur if any magnets themselves were notunder any coils at all times during the wave cycle, a situation thatshould if at all possible be avoided. The problem of underused coils canbe compensated in part by at least 3 methods to increase the averageindividual coil energy conversion efficiency: 1) One can design the WECto handle waves of the significant wave height that will be most likelyto be encountered in any given location and not the maximum possiblewave height that will be encountered. Then the stroke distance of therotor can be made shorter, less coils in the FCA would be needed, andfor a given rotor mass, magnets of greater radial axis length (diameter)and lesser longitudinal axis length (thickness) may be used, therebyconcentrating the total given amount of magnetic flux into a smallerspatial volume. One can only enlarge the diameter of the PMA magnets byso much, because if the ratio of the longitudinal axis length to theradial axial diameter of the magnets becomes too small, the flux lineconcentration B field along the perimeter of the magnets, i.e. thecylindrical surface of the PMA which is advantageous in itself with thenearby coil placement, may become so great that the repulsive forcesbetween the magnets may become problematical even with the stainlesssteel central support tube. Furthermore, the energy of the rarer largerwaves will be wasted to some extent; 2) If the magnet material volumeand mass are kept constant but the magnetic strength of the material isincreased (a higher N factor or megagauss-oersted factor), the totalmagnetic flux lines within the volume of the given number of FCA coilsis increased; 3) One can transition from a PMA whose longitudinal axislength is one third that of the significant wave height and strokedistance with 12 coils per magnet pair and 6 coils per magnet (condition2) to that which is one half of the significant wave height with 8 coilsper magnet pair and 4 coils per magnet (condition 1) which again withthe total magnet mass and volume kept constant increases the total fluxlinkages per individual coil of the FCA but at the expense ofsacrificing some of the kinetic energy in the form of a somewhatdecreased velocity imparted to the moving rotor element associated byadopting condition 1 over condition 2. The tradeoffs are difficult butshould be accomplished within the proviso that the main utilization ofseawall embodiments of the present principles is to mitigate the damagedone to structures upon which the waves impinge with an accompanyingconsequent production of electrical energy.

There is one important situation that can arise when the waves impingingon the WEC's of the EKS may be relatively small such as in a lake,estuary, bay, sound, or other calmer body of water or calm portion ofthe ocean. It was previously pointed out that the state of occurrence ofsuch small waves would invoke the preferred arrangement of 4 coils permagnet pair and pole piece pair whose combined width is equalapproximately to that of the width of the magnet pair and pole piecepair and this preferred arrangement would hold predominance over theother two conditions 1 and 2, calling for 8 and 12 coils respectivelyper magnet pair and pole piece pair, that become significant factorswith larger waves. Under this circumstance of small waves, theefficiency of wave kinetic energy as defined by the amount ofdissipation and conversion of such wave kinetic energy to electricalpower per FCA coil goes down drastically if the conditions 1 and 2 of 8and 12 coils per magnet pair and pole piece pair are applied. Thepreferred arrangement of 4 coils per magnet pair and pole piece pairdictates, with the presence of waves of small significant height, thatthe length of the FCA be only slightly longer than that of the PMA, andthat the difference in length be equal to the significant wave height ofthe waves. For this to hold, the longitudinal length of the PMA shouldbe significantly greater than that of the significant height of thewaves. In this manner, every magnet of a very long PMA can vibrate undervirtually every coil of a very long FCA just slightly longer than thatPMA dissipating wave kinetic energy even if the significant height ofthe waves is relatively small, resulting in the greatest kinetic energydissipation efficiency per PMA magnet and FCA coil together therebyallowing WEC's using long FCA and PMA lengths to dissipate considerablekinetic energy into electrical energy even with small waves beingpresent. This advantageous state is only achievable when the wavesignificant height is much shorter than either the length of the PMArotor or the FCA stator. It is important to note that as the ratio ofthe length of the PMA to the significant height of the waves gets largerfrom a magnitude of approximately 1:3 and approaches 1:1, the 12 coilcondition (condition 2) per magnet pair and pole piece pair, to bereferred to at this point as a PMA structural magnetic unit (SMU), ismost beneficial, and the 8 coil condition (condition 1) per PMA magneticstructural unit, becomes more beneficial to maintain the highestefficiency of kinetic energy conversion by the WEC. As the ratio oflength of the PMA to the significant height of the wave begins toincrease significantly past 1:1, the preferred arrangement of 4 coilsper magnetic structural unit comes into beneficial predominance for theadvantageous state of maximal wave kinetic energy dissipation and ismost advantageous as compared to the two other conditions 1 and 2 whenthis ratio is very high. It is important where possible to make thelength of the FCA in the stator for embodiment 1 of the VLEG greaterthan the sum of the significant wave height and length of the PMA in therotor to prevent some magnets of a PMA to be uncovered by coil windingsat certain times of the wave cycle. Furthermore, this ratio should notbe so high that the length of the WEC's PMA and FCA would be capable ofextracting more kinetic energy from the wave than the small waveactually contains—PMA's and FCA's longer than this, i.e. where thisdescribed ratio is very high, result in no increased energy conversion;not only would this state be simply a waste of coil winding copper andrare earth magnet material, but also the excessive mass of the PMArelative to the small wave input force exerted on the buoy floatationcollar by the small waves as well as an increased mass of the mobilesubunit containing the rotor relative to the mass of the fixed subunitwould impair the operation of the WEC.

Note that although the preferred first embodiment of the presentprinciples comprises a moving PMA rotor and fixed stationary FCA statorarmature, this discussion applies also to the second embodimentcomprising a moving FCA armature rotor and fixed PMA stator. It isbelieved that the above engineering considerations are much easier toachieve with the first embodiment. However, in either case, themultitude of parameters may be adjusted in accordance with theabove-described considerations to achieve an optimal mix of theseparameters so that the WEC may be used with effective function in anybody of water of waves of any height excluding storm high windconditions and calm water surfaces lacking the presence of discerniblewaves. It is believed that the flexibility of design of the parametersjust described as well as other parameters described elsewhere in thedescription of the present principles, which allow use over such a widerange of wave magnitudes, is novel and significant.

By way of illustration, for ocean waves of significant height, i.e. 2 to6 meters, for example, a WEC should have a PMA rotor whose length is setat 2 meters and an FCA stator whose length is 6 meters for highestefficiency of kinetic energy dissipation, keeping all other factors(magnet and coil diameter size, wire gauge, etc.) constant. Further,there should be 12 coils for each PMA structural magnetic unit. If thesignificant height of the waves was 1 to 2 meters, the FCA length may beadjusted to 4 meters with 8 coils per structural magnetic unit. Forwaves of 0.25 to 1 meter, the FCA length may be adjusted to 2 metersplus the significant height of the wave or 2.25 to 3 meters with 4 coilsper structural magnetic unit. Small waves of this level will still allowfor high efficiency of kinetic energy dissipation because, although eachmagnet of the PMA moves a small distance, all the magnets are alwaysmoving within the FCA coils and there are many coil magnet pairs activeat any given time. Note that waves smaller than 0.25 meter insignificant height would probably not contain sufficient energy to makefull use of a 2 meter PMA, as they would simply not contain sufficientenergy in the wavefront surface impinging on the WEC and, hence,efficiency will drop considerably. Note, however, that using all therelationships and conditions described so far that determine optimalconfigurations of coil widths, FCA and PMA lengths, and coil to magnetratios, even given waves of only 0.1 meter (10 cm.) in significantheight, a WEC can be constructed that can produce significant electricalpower from all the magnets and coils simultaneously. In this example,the WEC should have a 1.1 meter LCA stator (equal to the length of thesum of the PMA length plus the significant height of the wave)surrounding a 1 meter PMA rotor containing 10 structural magnetic unitseach 0.1 meter (100 cm.) in width with 2 magnets 0.035 meter (3.75 cm.)in thickness and 2 pole pieces of desired thickness (magnet thickness topole piece thickness in the preferred configuration ranges from 2:1 to8:1) relative to the thickness of each PMA magnet that are 0.0125 meter(1.25 cm) in thickness and with 4 coils of thickness 0.025 meter (2.5cm) for each structural magnetic unit results in the use of 20 magnets,20 pole pieces plus one extra end pole piece, and 44 coils. Theapplication of the EKS can gradually change from primarily coastalstructure protection from significantly sized waves to a primaryfunction of conversion of kinetic wave power to electrical power as thesize of the waves get smaller and are less destructive. This transitionof utilization is strikingly illustrated by this example and isrepresentative of a secondary function of EKS embodiments to produceelectrical energy from the kinetic energy of sea waves. Additionalcalculations for selecting the proper sized magnets and pole pieces forthe structure of the VLEG and WEC within the EKS operating in a givenwave environment will be described presently.

The efficiency of the VLEG can be further enhanced when the length ofthe PMA rotor employed in the optimal configuration of the VLEG of theWEC and the number of utilized electric power producing magnets, polepieces, and FCA coils are related to and designed for the desiredsignificant wave height H_(TE) of the waves that would be expected to beencountered most commonly. The preferred design is described as follows:s_(r), the rotor stroke distance, should approximately be equal to thesignificant wave height, H_(TE), and, as previously stated, optimalkinetic energy transfer to the rotor should be such that s_(r) should befor the larger waves three times the longitudinal axial length of therotor PMA. If T_(m) and T_(p) are the thicknesses of the electric powerproducing magnets and pole pieces respectfully that are to be employed,it can be shown that the optimal number of magnets and pole pieces inthe preferential configuration is equal to H_(TE)/3(T_(m)+T_(p)), theoptimal number of magnet pairs in repulsion field configuration is equalto H_(TE) /6(T_(m)+T_(p)) and the optimal number of coils in the statorarmature in the FCA of preferred width described above, which can beexpressed as equal (T_(m)+T_(p))/2, would be satisfying the second ofthe two above conditions and is given by 2H_(TE)/(T_(m)+T_(p)). In thismost preferential configuration for larger waves, there would be 6 coilsin the stator FCA armature per magnet or 12 coils per magnet pair in thePMA. In the less preferred configuration for large waves of a lessermagnitude where the stroke distance, s_(r), equal to the significantwave height, H_(TE), is twice the distance of the axial longitudinallength of the PMA rotor and would be satisfying the first of the twoabove conditions would result in H_(TE) /2(T_(m)+T_(p)) magnets and polepieces being used in the PMA and H_(TE) /4(T_(m)+T_(p)) magnet pairsbeing used, resulting in at least 4 coils in the stator FCA armature permagnet or 8 coils per magnet pair in the PMA, with the number of coilsused in the armature FCA stator again being given by2H_(TE)/(T_(m)+T_(p)). For smaller waves, the previously describedpreferred configuration of 2 coils with each magnet or four coils permagnet pair (PMA structural magnetic unit) would yield a number ofmagnets in the PMA equal to X_(PMA)/(T_(m)+T_(p)) and number of magnetpairs (SMU's) equal to X_(PMA) /2(T_(m)+T_(p)), where X_(PMA) equals thePMA longitudinal axial length that has no relationship to thesignificant wave height other than being significantly larger than thisheight. In this case the number of coils used in the FCA can be given by2(X_(PMA)+H_(TE))/(T_(m)+T_(p)). Note that for larger waves(H_(TE)>X_(PMA) or H_(TE)=X_(PMA)), the number of PMA magnets, polepieces, magnet pairs (structural magnetic units), and FCA coils arerelated linearly to the significant wave height, H_(TE), (equal to therotor stroke distance s_(r)) for any given magnet thickness, T_(m), andpole piece thickness, T_(p), such that the preferred ratio ofT_(m):T_(p) ranges from 2:1 to 8:1, a range based upon engineering andassembly factors to be explained in detail when the CompressiveRepulsive Magnetic Field Technology that comprises the structure andfunctioning of the PMA is described; for quite small waves(H_(TE)<<X_(PMA)), the number of magnets, pole pieces, and structuralmagnet units magnet pairs are related only to X_(PMA), T_(m), and T_(p)and are independent of both T_(HE) and s_(r) while the number of usedcoils in the FCA does depend on H_(TE) and X_(PMA); for waves of mild tomoderate size (H_(TE)<X_(PMA) approximately), any of these arrangementswould be acceptable. A similar calculation for the number of magnets,magnet pairs in the PMA, and coils in the armature could be done if thestator was the PMA and the rotor was the FCA armature.

The design of the PMA 37 in the embodiment depicted in FIG. 3A calls forspecially designed magnets with a central hole 47 through the magnetsthat allows the multi-strand stainless steel, mono-filament Kevlar orother suitable material composing flexible suspension cable 33 to travelthrough the PMA and be attached to it via knotted or suitable othermeans. Central hole 47 in conjunction with structural stainless steelsupport tube 36 in FIG. 3A performs at least 6 functions: 1) allows thePMA to be attached to the mobile subunit 19 via attachment points atbreaking magnets 74 and 75 of FIG. 7B so that kinetic wave energycaptured by the latter can be transferred to the rotor when the rotor isthe PMA, the preferred embodiment. 2) Allows the anchoring of the springsuspension system—at point 80, the lower end to the fixed subunit 20containing the stator via the lower restorative force spring 63 in FIG.7B and the upper end at point 58 to the mobile subunit 19 when the PMAis the rotor. 3) Allows for structural stability of the PMA by allowingthe stainless steel tube backbone to be bonded to each pole piece andmagnet of the PMA. 4) Allows for the PMA to be structurally supported bythe central tube when the PMA is the stator and it must be securelyfixed to the fixed subunit 20 at point 80 as in FIG. 7A. 5) Especiallyimportant for long rotor PMA's with many magnets is that the centralhole serves as a conduit of air that allows equalization of airpressures above and below the PMA as it slides in slotted sliding tube32, a factor which if not accounted for, would greatly slow the rotorPMA in its vertical oscillation due to serious air drag and resistancewhich would seriously oppose the rotor's relative motion to the statorwith the same negative effect as Lenz's Law counter EMF losses reducingelectrical power output and efficiency; without the central hole, thisserious drag and resistance problem would only otherwise be amelioratedinadequately through the thin space of the air gap 61 on FIG. 7B. In thecase of the slotted metal rotor sliding tube, the slot also shares someof the function to equalize the air pressure above and below the rotoras it slides in the tube. The PMA is bonded to the outside surface ofthe stainless steel support tube, and though the central channel 47 hasthe stainless steel or Kevlar suspension cable running through it,sufficient airspace remains in the central hole 47 to allow excellentair pressure equalization to take place. 6) Though not part of therotor, the braking magnets in both embodiments of the VLEG in the WEChave central holes so as to allow the passage of the suspension cablethrough them.

Note that the efficiency of any linear electric generator is adverselyaffected by a parameter known as parasitic damping which degradesmechanical transfer of energy of the wave to the rotor. It is governedby 4 factors minimized in the present invention: 1) Sliding frictionminimized by the use of sliding bearing surfaces, lubricants, and smootheven electropolished surfaces at the sliding rotor tube PMA air gapinterface; 2) Thermoelastic losses in the springs minimized by the useof relatively stiff springs; 3) Air resistance encountered by the rotorminimized by the central hole structure in the PMA, the slot in thesliding rotor tube, the end air vents in the non-slotted non-conductiveplastic sliding rotor tube, and 4) Compensatory reactive vibration ofthe fixed subunit in response to the ocean wave input force minimized bya very high ratio of the mass of the fixed subunit to the mass of themobile subunit and positioning of the center of gravity of the fixedsubunit at a significant depth beneath the ocean surface. Parasiticdamping must be equal to another critical parameter for maximum poweroutput from a VLEG, the electromagnetic damping which will be discussedin the detailed description of the basic VLEG unit below.

The distance across which the rotor oscillates, the stroke distance,should equal the significant height of the largest waves designed to behandled by the WEC. Specifically, this height is equal to the distancefrom the trough to the crest of an equivalent wave, which is defined asthe average of one third of the tallest waves likely to be observed atmost times measured during a designated time interval. Optimally, asnoted above, this height is three times the axial length of the PMArotor, which should be one third the height of the average equivalentwave height just defined. Note that if the EKS apparatus is an arraythat comprises more than one row of WEC repeating units, then the energydissipation function can be shared by each row. For instance, to have areasonable amount of energy to be dissipated from a 2 meter high wave, aWEC with a rotor stroke distance of 2 meters and a rotor of 0.66 meter(66 cm) in axial length should be used. However, an EKS apparatus arrayconsisting of 10 rows of WEC repeating units can employ a rotor strokevolume theoretically of only 0.2 meters and a much smaller rotor of 6.6cm in axial length to dissipate a significant fraction of the energydissipated by the larger unit. Thus, a few large WEC's packed fairlyaway from each other can be advantageously, in terms of engineeringdesign, substituted by many small WEC's packed very closely together, asignificant novel characteristic of the present principles.

Normally, unless the fixed subunit 20 is rigidly attached to the seafloor or to the adjacent conventional sea wall, as the mobile subunit 19and consequently its contained rotor oscillates vertically in responseto the passage of the wave, the fixed sub unit 20 will tend to oscillatealong with it, greatly diminishing the relative velocity of the rotorPMA 37 with the stator FCA 34 contained within the fixed subunit,thereby markedly decreasing the power output because the latter isneutrally or slightly positively buoyant and will try to oscillate withthe passage of the wave as well. In addition, the counter EMF force dueto Lenz's law acting on the rotor PMA will also tend to cause the fixedsubunit to oscillate undesirably relative to the rotor PMA.

To circumvent this difficulty, three approaches were taken in thepreferred embodiment so that the input force by the wave on the fixedsubunit 20 was minimized as much as possible relative to the wave inputforce on the mobile subunit 19. First, since the wave input force on anybuoyant object is proportional to the area of buoyancy material ofbuoyant object exposed to the wave, the fixed subunit buoyancy component30 FIG. 3A was made long in its vertical axis, and narrow in itsdiameter. Second, the ILWDS 22 was designed to create a very hugereaction mass compared to the reaction mass of the mobile subunit 19causing the amplitude of any oscillation of the fixed subunit 20 to bevery small compared to that of the mobile subunit 19 even if the WECcomponent is just floating and not even tethered. Third, as explainedpreviously, the center of mass and gravity was designed to be centeredin the ILWDS 22 that was placed to a significant depth beneath thesurface of the ocean by the long stem of the fixed subunit 20 where wavemotion water particle oscillations are markedly diminished in amplitude.

Again referring to FIG. 3A, the Inertial Liquid Wave Dampening System(ILWDS) functions with features similar to heave plates but alsocontaining novel new features; it's nomenclature is based upon theentrapment of a large mass of liquid within the structure to act toalmost completely dampen the oscillatory effect on the fixed subunit ofthe waves at the ocean surface. The inertial wave dampening mechanismcan be attached to the stator of the WEC and can comprise a weightcontainer including at least one ingress hole, such as 41, configured todraw water into the container to thereby attain sufficient weight tostabilize and render the stator relatively stationary in response towaves. For example, the ILWDS in FIG. 3A comprises a stack of two ormore metal heave plates with skirts 8 braced together by metal brace 9.The metal skirts impede the motion of water in the vicinity of the heaveplates helping to dampen out vertical oscillations from the waves aboveat the surface. The bottom heave plate 8 is attached to a water filledlarge weight 10. Heave plates with metal weights can perform a similarfunction, but a water filled weight has the distinct advantage of beingmassive in extent, but does not become a functioning part of the WECuntil it is deployed in the water. When it is deployed, the WEC isallowed to sink to the desired depth with the entrance of water intoweight 10 via bottom water ingress and egress holes 41 that are severalin number with two being shown. As water enters the chamber of weight10, the WEC sinks to its near neutral buoyancy point and adjusted to beslightly positive in buoyancy for increased stability at the desireddepth. The water ingress into weight 10 is gradual, and thus the WECsinks gently into its desired position. This arrangement allows for mucheasier transport of the WEC to its desired location as weight 10 willremain empty of water during transport, and the weight of the ILWDSstructure 22 will consist of only the metal weight of heave plates 8,brace 9, and the metal chamber of weight 10. Furthermore, a novelmechanical means is provided to re-float the WEC back to the surfaceshould it be necessary for maintenance or replacement. Here, the ILWDScan include a tube 200, 202 coupled to the weight container having alength sufficient to extend an end of the tube above a surface of theocean when the stator of the WEC is at least partially submerged in theocean or when the container is filled with water. The tube can beconfigured to be attached to a pump mechanism for expelling water fromthe container when the stator is at least partially submerged in wateror when the container is filled with water. In the particular exampleillustrated in FIG. 3A, the re-float mechanism can be implementedthrough the introduction of air under pressure via rubber or plastic airhoses 200, 202, the latter attached to an air pump at the surface, airvalve 201, and air ingress and egress hole 199; water is expelled out ofholes 41. When the process needs to be reversed, this system isdisconnected from the air pump and water once again ingresses intoweight 10 forcing out the air previously introduced out via air hoses200, 202 and air valve 201. This setup is clearly advantageous overweighting down and stabilization techniques for floating verticallyoriented WEC devices. The combined mass of entrapped water in weight 10,the weight chamber itself, the heave plates, brace, and the waterentrapped within the skirts are a huge reaction mass incorporated intothe fixed subunit 20 relative to the reaction mass of the mobile subunit19, a most desirable configuration. The ILWDS prevents the fixed unitfrom oscillating vertically even with large waves passing through theWEC above. It should be noted that it is important to have the center ofgravity of the fixed subunit 20 of the WEC which is located in the ILWDS22 structure to be as deep below the ocean as possible below and awayfrom the buoyancy point because it can be shown that the horizontalforce and velocity vectors for the water and the much more importantvertical force and velocity vectors as well as the ocean surface waveenergy density decrease with the square of increasing depth below theocean surface; this factor is of major importance along with the largemass ratio of the fixed subunit 20 relative to the mobile subunit 19 inkeeping the fixed subunit as immobile as possible so that the mobilesubunit can develop the highest relative velocity in the rotor relativeto the stator of the WEC repeating component of the EKS.

Again referring to FIG. 3A, the electromechanical braking systemcomprises: cylindrical rare earth NdFeB braking magnet 28A with centralhole 64 and lower braking magnet 28B with central hole 59A through whichstainless steel multi-strand cable 59 passes (central hole 59A alsoextends through fixed subunit top 5); upper very large gauge copperbreaking coil 31A and its lower counterpart 31B that are intermittentlyelectrically short-circuited; tapered stainless steel upper compressionspring 192 whose upper end is attached to the lower surface of fixedsubunit top 5; and stainless steel extension spring 63 previouslydescribed to be attached to PMA 37 and the top surface of the ILWDSheave plate skirt at attachment point 39B through cable 59 passingthrough braking magnet 28B. Note that upper braking magnet 28A iscompletely contained within the coils of compression spring 192 and thatextension spring 63 serves the dual purpose of being part of the VLEGlinear rotor's suspension system as well as part of theelectromechanical breaking system. Furthermore, the polarity of eachbreaking magnet is the same as the facing end of PMA 37.

The electromechanical breaking system functions to limit the excursionof the linear rotor on the spring suspension system in the event ofextremely large waves impinging upon the WEC by avoiding damage byexcessively severe oscillation by waves exceeding the ability of the EKSto safely encounter. It comprises 3 functional components. The firstcomponent is electromagnetic and comprises large heavy gauge coppercoils 31A and 31B that are wound around the upper and lower ends ofslotted rotor sliding tube 32 respectively and are electrically shortedout on an intermittent basis; slotted rotor sliding tube 32 is part ofthe support structure for stator formed by FCA 34 which also includesthe upper surface of the upper heave plate 8, outer water tight tube 29and the bottom surface of the top 5 of the fixed subunit 20. The brakingcoil 31A and/or 31B, when short-circuited, imposes acounter-electromotive force on the permanent magnetic array in the rotorof the WEC as the array approaches the coil when the coil isshort-circuited. For example, when electrically shorted, very largecurrents are induced within the end braking coils 31A and 31B by theapproach of a strong magnet such as PMA 37 because of the very largewire diameter and short total length of wire involving just a few coilwindings. As illustrated in inset FIG. 3A(1), these coils couldequivalently be replaced by a thick ring of copper or suitable otherconducting pipe which would accomplish the same effect of producing avery large current as the PMA 37 approaches resulting in a very largeback EMF (electromotive force) that helps break the moving PMA to astop. The second component is elastically mechanical and comprisestapered compression spring 192 on the top of the stator and extensionspring 63 at the bottom of the stator mechanically decelerate the fastmoving rotor upon its approach to the top and bottom ends of the statorrespectively. Note that compression spring 192 collapses around brakingmagnet 28A that is contained within the coils of this spring. Note alsothat extension spring 63 serves the dual function of braking the rotoras well as assisting the rotor as it begins its down stroke on the startof the negative slope half of the wave. The third component is purelymagnetic and comprises a repulsion field magnetic braking process; whenthe PMA 37 gets too close to either braking magnet 28A or 28B, becauseend poles of PMA 37 have the same polarity as the braking magnet polesthat they respectively face, upon reaching the proximity of the brakingmagnet, the rotor is repelled away again decelerating it.

Note that the ends of the PMA are formed by thinner end magnetic fielddeflecting magnets 212 and 213 as compared to the thicker magnets 40that compose most of the PMA. Magnets 212 and 213 have at least twofunctions. First, they are used to bend back and focus magnetic fluxlines that exit out of and into the PMA and that are parallel or almostparallel to the long axis of the PMA; this function will be described ingreater detail later. Second, because the outer poles of magnets 212 and213 are of the same polarity as the poles of the end braking magnets 28Aand 28B that they face respectively, the PMA is decelerated as itapproaches the end braking magnets secondary to the action of a largewave. Unlike the thicker magnets 40, their primary function is not todissipate wave kinetic energy into electrical energy but rather to bendand focus the end magnetic field of the PMA back onto the PMA onto aninterior opposite polarity pole. In small enough WEC structures, magnets212 and 213 may be omitted as the focusing function can be accomplishedby the breaking magnets 24A and 24B themselves while repelling the endsof the PMA if it approaches too closely. It should be noted thataddition of the end magnets 212 and 213 led to a 20% improvement in themagnetic field intensity in the areas of the field coil array, as theend magnets significantly reduced the amount of magnetic field linesthat were lost to empty space.

This partly electromagnetic, partly mechanical, and partly purelymagnetic brake that is comprised within the WEC has 3 distinctmechanisms are used rather than only one to brake an excessively movingrotor. Mechanical bumpers of hard rubber and other materials that can beused to mechanically and abruptly stop the rotor produces excessiveenergy loss from collision friction losses and a shorter lifespanbecause of the mechanical wear and fatigue. To avoid this type ofmechanical wear, as noted above, embodiments of the present principlesmake use of a counter EMF short-circuited coil or circular plate (pipesegment) to brake the oscillating rotor. Unfortunately, this has thedisadvantage of dissipating the energy of the rotor as wasted heat,reducing the efficiency of the device. To minimize this problem,embodiments employ a repulsive magnetic braking technique that uses themagnets themselves on the ends of the rotor, which have the samepolarity alignment as braking magnets within the stator to cause theexcessive kinetic energy of the rotor to be temporarily stored withinthe repulsive magnetic field as potential energy. This energy can bereturned to the rotor upon the passage of the excessively high wave andused to generate electrical power. Furthermore, a spring system, throughspring compression and expansion, not only mechanically slows down therotor upon its arrival at the ends of the stator, but, as in the case ofthe magnetic breaking, captures the kinetic energy of the rotor andchanges it to potential mechanical energy stored in the springs; bothquantities of potential energy from the magnetic braking mechanism andthe mechanical braking mechanism are able to be returned to the systemonce the large wave passes. Note also that the electromechanical brakingmechanism greatly softens the impact on outer sliding tube 27 of FIG. 3Aas it impinges upon the rubber blocking bumper ring 25 when theapproaching crest of a wave of the largest size for which the WEC isdesigned or larger occurs, preventing wasted energy due to frictionalheat losses and undesirable structural stress on the WEC, which is aproblem with the single bumper impact braking methodology. As the outersliding tube 27 approaches bumper ring 25, at the same time, the rotoris approaching the electromechanical braking mechanism. A similarbraking effect on outer sliding tube 27 impacting on bumper ring 5Aoccurs when the trough of an excessively large wave approaches.

One other function of the end braking magnet is to focus and redirectmagnetic flux lines flowing into and out of the ends of the PMA backinto the interior poles of the PMA greatly minimizing the flux wastageand leakage into space as shown on FIG. 9C and FIG. 9D. This dualbraking and focusing effect, which will be explained in greater detailbelow, occurs if the stroke distance of the rotor is not too large alongits axis of vibration with respect to the size of the end brakingmagnets and reach of their magnetic fields. In fact, an advantageouscondition will occur. For example, as a PMA without end magnetic fielddeflecting magnets approaches the end braking magnet, the magnetic fieldlines escaping into space are bent back to a greater and greater extentonto interior coils of opposite polarity in the PMA, which to someextent increases the electrical power produced as the rotor deceleratesat the trough and crest of a larger wave where it is more likely to bein close proximity to the end braking magnet; this effect would not beapplicable to PMAs whose ends have end magnetic field deflecting magnetswhich are advantageously used for rotors with large stroke distances.

Additionally, another distinguishing feature of the electromagneticbraking component embodiment is that it minimizes the ohmic heat lossesusing a novel technique to quickly switch automatically the brakingcoils between an open circuit state and short circuit state so that theheavy gauge wire windings are shorted and dissipate energy only whenencountering an excessively large wave that could potentially damage thesystem. The switching mechanism is shown schematically as component 203FIG. 3A for the upper braking coil and not shown for the lower brakingcoil for ease of illustration, and comprises either positional mercurytilt switch or other type of position sensor 203, including a switch203A and a position sensor 203B, and is placed across the outputs of thebraking coil windings so that the coil windings are short circuited whenthe switch 203A is in a closed state only with the passage of a singlelarge wave of a given size and at no other time. The position sensor203B is configured to sense a tilt of the converter and activate theswitch 203A to short-circuit the coil in response to sensing that thetilt exceeds a threshold. In one exemplary embodiment, the threshold canbe set to a value at or between 60 to 90 degrees. For instance, thedesign application used may call for waves higher than a given heightproducing approximately at or greater than a 60 to 90 degree tippingfrom the vertical of the buoy floatation collar top 26 being consideredan unacceptable mechanical stress to the WEC; such a condition wouldactivate the position sensor 203B of the mercury tilt switch 203, shortcircuiting the coil windings; once the wave passes, further wavessmaller than this would keep tilt switch 203 open keeping the brakingcoils open-circuited avoiding any possible losses of energy throughunwanted partial braking from smaller waves. Referring to the inset FIG.3A (1), if a section of copper pipe 206 was used instead of the heavygauge wire coils windings, a slit 207 can be placed in the pipe sectionalong its length, the two sides of which would be connected to switch203; if the tilt switch or position sensor was activated, the slit edgeswould be shorted together activating the electromagnetic brakingprocess. This feature of automatic switching in and out the shortcircuit state of the braking copper coils or the solid copper ring is aparticularly advantageous aspect provided by the present principles.With this novel three-part breaking mechanism, at least some fraction ofthe kinetic energy of even an excessively large wave can be dissipatedand captured temporarily to be then converted to electric energy insteadof having all of the energy of that wave wasted as ohmic resistancelosses.

FIG. 7A and FIG. 7B shows the two different exemplary embodiments of theVLEG constituting the power conversion mechanism of the WEC repeatingcomponent of the EKS. FIG. 7A shows the embodiment in which the statoris PMA 37 and the rotor is FCA 34. FIG. 7B shows the embodiment in whichthe rotor is PMA 37 and the stator is FCA 34. The two differentembodiments are functionally identical; the functional description ofembodiment of FIG. 7B has already been described in detail with thedescription of the WEC of FIG. 3A, and thus, the detailed functionaldescription of the embodiment of FIG. 7A will not be repeated as thesimilarity is apparent to experts in the field of linear electricgenerators. Note that the embodiment of FIG. 7B differs from FIG. 3Aonly by the fact that the lower extension restorative force spring 63 isseparate from a second compression spring 208 functioning as a brakingspring whereas in the description of FIG. 3A both the braking andrestorative force functions were carried out by single spring 63. Also,in FIG. 7A, coil windings going out of the page are designated 34C andcoil windings going into the page are designated as 84, while in FIG.7B, they are designated 82 and 34D respectively. The embodiment of PMArotor 37 and FCA stator 34 is the preferred embodiment as was explainedpreviously. The PMA stator sits stationary on its support tube and theFCA rotor and its supporting slotted rotor slide tube slides in avertically oscillating manner in the second embodiment versus the PMArotor oscillating vertically and the FCA stator remaining stationary onits supporting slotted rotor sliding in the first preferred embodiment.

Structurally, the preferred embodiment of the PMA rotor, FCA stator VLEGshown in side view in FIG. 7B is as follows: PMA 37 containing end steelpole pieces 60 and 62, interior steel pole repulsive field pole pieces53, magnets 48 and is attached to cable 33 at its upper and lower points76 and 76A respectively and cable runs through PMA 37 inside supporttube 36 via central hole 78 of each magnet and pole piece though whichsupport tube 36 runs. Cable 33 is attached to the lower end of upperperturbing force spring at point 73 which in turn is attached at itsupper end by cable 59 to reaction mass (2), the mobile subunit, (notshown) at attachment point 58. Braking magnets 74 and 75 with centralholes (not labeled), tapered compression springs 192 and 208 attached tothe top and bottom of ends of rotor sliding tube 32, and large gaugeshort circuit coil windings 31 at either end of rotor sliding tube 32constitute the electromagnetic, mechanical, and purely magneticcomponents of the rotor braking mechanism. The FCA is wound aroundsliding tube 32 with coil windings 34D going into the page, and coilwindings 82 going out of the page. The lower end of cable 33 is anchoredto the bottom end of rotor slide tube 32 at the upper point ofattachment 79 of lower restoring force spring 63. Rotor slide tube 32 isanchored to reaction mass (1) which would be the fixed subunit of theWEC at attachment plate 65.

Structurally, the second embodiment of the VLEG of the WEC with the PMAstator and the FCA rotor is shown in side view in FIG. 7A as follows:upper perturbing force spring 23 is attached to the reaction mass (2),the mobile subunit, at attachment point 58 and to the top of the FCArotor at attachment point 76B via cables 59. The PMA stator 37 is halfway up a long support tube that not only travels through its centralchannel 47 (not shown) to provide structural support but also keeps thePMA in a stationary desired location at the middle of the FCA during theneutral point of the wave. Upper and lower tapered compression brakingsprings 192 and 208 respectively are as in the first, preferred,embodiments with their associated attachment points. Cable 33 and itsattachment points are not present. Braking magnets 74, 75, shorted largegauge coil windings 31, FCA windings 84 and 34C into the page and out ofthe page respectively, lower restorative force extension spring 63attached to the bottom of the FCA rotor at its upper end and to thereaction mass (1), the fixed subunit, at its bottom end 65 at attachmentpoint 80 are all as per the first embodiment. Note that the lowerbraking magnet 75 fits completely within the coils of the lower brakingspring 208 in both embodiments. The stator PMA 37 comprises the samecomponents as the rotor PMA 37 of the first embodiment.

In order to have the above operation of embodiments of the presentprinciples occur with a reasonable degree of efficiency, and operationaldurability, and be applicable to a wide variety of environments andapplications, several features should be incorporated into the EKSapparatus. The type of LEG that is used within the repeating componentWEC of the EKS, which has been assigned the nomenclature “VibrationalEnergy Generator” or “Vibrational Energy Transducer” and “VibrationalEnergy Linear Electric Generator” (VLEG), includes several novelaspects, and together with the embodiments employed to protect seacoasts, harbors, and shoreline structures and property, establishes anew aspect of the technology in the field of environmental coastal andshoreline protection as well as the field of vibrational energyharvesting. Several of these features are further described in detailherein below.

The VLEG

The VLEG is a “vibration responsive electrokinetic transducer” thatforms the heart of the wave kinetic energy dissipation to electricenergy apparatus of the repeating unit Wave Energy Converter (WEC) ofthe Electrokinetic Sea Wall (EKS) apparatus that constitutes embodimentsof the present principles. Though the VLEG may be used to convertvibrational mechanical energy of many types such as the energy ofcrashing surf, a large vehicle bouncing on a road, the wind oscillatinga moving mass, etc., for expository purposes, the VLEG is described as acomponent for transforming undesirable wave kinetic energy into usefulelectrical energy, thereby not only permitting the present principles toserve its purpose of protection of structures exposed to wave movements,but also its purpose of producing electrical energy for useful work. TheVLEG comprises a basic unit that is adapted to use as a component ofboth the moving rotor of the mobile subunit of the WEC and thestationary stator of the fixed subunit. It comprises five important,distinguishing components and can be used in a unique 3-dimensionalorganizational matrix structure: 1) a spring suspension system; 2) Aunique technology that is given the nomenclature, “Compressive RepulsionMagnetic Field Technology; 3) A variable wire gauge copper coil windingarrangement; 4) A method of magnetic focusing of lines of flux onto thecopper coils for enhanced production of electric energy from a givenamount of vibrational kinetic energy; 5) A method for placing manyVLEG's in parallel in a three dimensional Electrokinetic TransducerMatrix for much greater power output. Each one of these aspects of theVLEG will be described in succession below. In addition, several novelarrangements by which many of these devices may be placed inElectrokinetic Sea Wall apparatuses of varied configurations todissipate the kinetic energy of waves over a large area of ocean surfaceof varied geometric shapes into useable electric energy will be furtherdescribed.

The Basic VLEG Unit

Referring to side view FIG. 9A and top cross sectional view 9E depictingthe first embodiment of the basic VLEG unit, the VLEG is composed oflinear rotor 81 in turn composed of PMA 37 now designated as reactionmass (3) comprising end pole pieces 51 and 54, repulsive field middlepole piece 53 sandwiched between two similar south poles, andcylindrical rare earth NdFeB magnets 37A and 37B with all of thesecomponents having a central hole 47, ¼″ in diameter, and through whichruns a stainless steel hollow support tube 36 of 0.24 inch O.D. andthickness of 0.01 inch. Brass and other stiff nonmagnetic metals aresuitable, and these dimensions can be changed depending upon thedimensions of the VLEG and its magnets and coils that are used. Throughcentral tube 36 runs a multi-stranded flexible stainless steel or Kevlar(or any suitable flexible material of high tensile strength) cable 33attached on the bottom of the cable at 79 to stator restoring forceextension spring 63 which in turn is attached at point 80 to reactionmass (1) 65. Reaction mass (1) may be the sea bed, the ILWDS heave platestructure with a large water filled weight as described in FIG. 3A, alarge anchor, a conventional sea wall or some other very large mass. Theupper end of cable 33 is attached at point 73 to the lower end ofperturbing force extension spring 23 whose upper end is attached atpoint 72 to reaction mass (2) (not shown in FIG. 9A but would be amobile mass that is oscillated in the vertical direction by a suitablesource of kinetic energy, which in the present embodiment would be themobile subunit 19 buoy floatation collar of FIG. 3A). Reaction mass (1)should be many times greater in mass than the sum of the reaction mass(2) and the mass of the PMA designated as reaction mass (3) in orderthat PMA 37 attached to reaction mass (2) via cable 33 and spring 23,can develop sufficient velocity relative to reaction mass (1) which isimportant for the VLEG to operate properly. PMA 37 reaction mass (3) isattached by knotted, bonded, or other means to cable 33 at both theupper and lower ends at points 76 and 77 respectively so that asreaction mass (3) oscillates in a vertical direction in response to thesource of kinetic energy; the oscillation is carried through by spring23 and transmitted to PMA 37 reaction mass (3) by means of cable 33being rigidly attached to PMA 37. If the attachment is by means ofbonding, the bonding is done with a magnetic epoxy, J B Weld®, or itsequivalent with a bond strength of at least 3500 lb. per sq. inch so asto insure the uniform distribution of magnetic flux across the centralhole at each of the two attachment points 73 and 77 and the magneticflux through the magnetic epoxy helps improve the strength of the epoxybond between cable 33 and PMA 37. The cable could also be attached via aknot on each end of the PMA or through the use of a small clamp that isbonded to each end of the PMA.

This first embodiment of the VLEG may be optionally contained in a shellformed by a rigid metal or Lexan polycarbonate material comprising anouter cylinder (for clarity not shown here in FIGS. 9A and 9B but isshown on FIG. 3A as 29) and would be used for adverse environmentalconditions. The VLEG is encased by this cylindrical shell along with topplate 74A, and bottom plate 74B which would enclose FCA linear stator82, formed by copper field coil array (FCA) 34 attached to and supportedby slotted rotor slide tube 32 whose lower end is rigidly attached toreaction mass (1) 65. The slotted rotor slide may be of any non-magneticmaterial, preferably stainless steel, brass, or polycarbonate plastic,and the slot 32A, shown in the cross section view illustrated in FIG.9E, runs vertically down the length of the rotor slide tube, and isseveral mm in width. The slot width is adjusted to make sure that therecan be no chance of contact with each edge during rotor motion whichwould nullify the marked reduction of eddy losses that this slot isdesigned to prevent. It is also adjusted by flexing slightly the wallsof the sliding tube to increase the inside diameter of the sliding tubejust slightly so that the rotor slides in the tube with the leastfriction possible and the smallest possible air gap between the magnetcylindrical surface and the inner slotted tube wall. The slot alsoallows for adjustment of the air pressure differential that occurs aboveand below the PMA as it slides in the tube which is detrimental as itopposes the development of the velocity of the rotor secondary to airentrapment ahead of the rotor. The slot may be omitted if slotted rotorslide tube 32 is made of non-conductive material such as polycarbonateplastic as there would be no eddy losses in the tube 32 if it isnon-conductive, but the slot may still prove desirable for the otherpurpose of adjusting the inside diameter of the tube to match closelythe outside diameter of the magnets of the PMA for air gap and slidingfriction loss optimization as well as air pressure equalization aroundthe rotor. If the slot is omitted, on a plastic sliding rotor tube, twosmall air vent holes not obstructed by FCA windings, one on either endof the slotted sliding tube, shown as air vents 214 in FIG. 3A, shouldbe created for air pressure equalization. Finally, cylindrical magnets74 and 75, each with an inside hole 48, ¼″ in diameter, through whichcable 33 passes, are attached to the top 74A and bottom 75A of thelinear stator shell formed with slotted rotor sliding tube 32. Air gap61 represents the space between the FCA stator 34 and PMA rotor 37. Boththe central hole 47 and support tube 36 may be of varying dimensions iflarger or smaller versions with different sized magnets and pole piecesare desired.

In a particularly desirous configuration, the slot 32A is made as narrowas possible consistent with a suitable inside diameter of the metalsliding tube 32 so as to allow efficient and easy sliding of theenclosed PMA 37 with the smallest air gap 61 possible, and if air vents214 are added in this case to maintain air pressure equalization evenwith a metal slotted tube, the slot may be filled in with anon-conducting epoxy that maintains the sliding tube 32 in anon-electrically conducting state for preventing eddy currents whichwill have the beneficial effect of both allowing the PMA 37 to slidealong the lubricated inner tube surface on a cushion of air, greatlyminimizing constant contact of the outer cylindrical surface of the PMA37 with the tube's inner surface, greatly reducing sliding friction andall of its resulting undesirable characteristics explained in detailelsewhere within the description of the present principles, and allowingthe sliding in such a manner so as to minimize the amount of Lenz's Lawcounter EMF opposing this motion through the prevention of eddy currentsin the sliding tube because of the tube's non-conducting state from thepresence of the slot preventing a complete electrical circuit in thetube thus preventing such currents from occurring.

The FCA 34 surrounds the PMA 37 and is wound on and supported by slottedrotor tube 32. There are 4 separate coils that are designed using avariable gauge wiring technique to be described subsequently andcomprising an outer layer of thick gauge wire 34A and an inner layer ofthin gauge wire 34B. The preferred but not exclusive arrangement ofthese coils is to have their total combined width approximately equal toor just slightly larger than the length of the cylindrical axis formingthe VLEG basic unit PMA. Thus, each coil has a width of one fourth thatof the length of the PMA cylinder. The inner diameter of the coil is setby the diameter of the slotted rotor tube, and the outer diameter of thecoil depends on the design dimensions, including magnet size and thepresence of any adjacent coils as will soon be illustrated anddescribed. Each FCA copper wire coil has inner coil windings of athinner gauge wire and outer coil windings of a thicker gauge wire. Thebasic VLEG unit PMA structure comprises two magnets in repulsive fieldalignment, one end pole piece, and one repulsive pole piece, henceforthto be called one VLEG PMA magnetic unit structure, plus one additionalend pole piece.

Referring to side view FIG. 9B and top cross section view 9F,illustrated is the second embodiment of the VLEG where the rotor is theFCA 34 that is a component of and attached to reaction mass (2), themobile subunit 19 in the present embodiment, and the PMA 37 is thestator 83 attached to and is part of the much more massive reaction mass(1) which in the present embodiment is part of the fixed subunit 20attached to that mass. In this version of the VLEG, there is no cable 33in the stainless steel tube 36 that lies in the central hole 47 of themagnets of PMA 37 (part of reaction mass 1); reaction mass 3, the rotor,is composed of top plate 74A, bottom plate 74B and the slotted FCAsupport tube 32 all of which may be any non-magnetic metal orpolycarbonate or other durable plastic stainless steel being thepreferred material; upper perturbing force spring 23 is attached at thebottom to the top 74A of the linear rotor shell at attachment point 73and at the top, to the mobile reaction mass (2) at attachment point 72;lower restoring force spring 63 is attached at the top to attachmentpoint 79 the bottom of linear rotor shell 74B and at the bottom to thelarge reaction mass (1) at attachment point 80; Braking magnets 74 and75 are again attached to the inner surfaces of top 74A and bottom of therotor shell 74B respectively although there is now no need for centralhole 78 in upper braking magnet 74 as no cable runs through it; lowerbraking magnet does have central hole 78 through which stainless steelsupport tube 36 passes. The FCA is supported by and is attached toslotted tube 32. Again, 61 is the air gap between the FCA rotor 34 andthe PMA stator 37. As before, FCA 34 has an outer layer of thick gaugewire 34A and an inner layer of thin gauge wire 34B. Again, thisembodiment can also be enclosed in a metal or durable plastic shell (notshown) that would enclose the VLEG in adverse environmental conditionsas described under the first embodiment. Note that the encasement shellstructure delineated in FIG. 10A enclosing a Vibrational EnergyElectrokinetic Matrix Transducer, of which the basic VLEG unit is thesimplest version, describes the mechanism by which a VLEG of eitherembodiment maybe enclosed within an environmentally protective casing;its description shall follow subsequently when embodiments the VLEGmatrix structure are described. The remaining structures of FIG. 9B ofthe second embodiment are identical to those structures previouslydescribed in FIG. 9A of the first embodiment.

Both embodiments of the VLEG implementations described above areequivalent linear electrical energy generators operating on the sameprinciples of Faraday's Law as applied to LEG's, and function inessentially the same manner. Thus, the function of the VLEG of FIG. 9Bwill not be spelled out in detail as is the case of the first embodimentas it would result in a virtually identical description. It is apparentto those skilled in the art LEG technology and electric energygeneration that the two embodiments function similarly. It is emphasizedthat either embodiment of the VLEG can function in the WEC repeatingunit of the EKS apparatus and all of the applications and embodiments ofthe present principles described herein. However, it is deemed that theembodiment where the linear rotor uses the PMA and the stator uses theFCA is the preferred embodiment, and henceforth, aside from FIG. 7Awhich shows incorporation of the second embodiment of the VLEG and FIG.7B which show the incorporation of the first embodiment of the VLEGbeing used in the WEC repeating unit of the EKS, subsequent drawingswill refer only to EKS apparatus variants that show the first embodiment(PMA rotor-FCA stator) of the VLEG. Those skilled in the art wouldunderstand that the WEC shown by FIG. 7B already described both in termsof function and structure in detail, is quite similar to the functionand structure of the WEC shown in FIG. 7A, so this detailed descriptionwill be omitted for the sake of brevity; furthermore, since theelectrical functioning of the VLEG basic unit of the first embodiment issimilar to the detailed electrical functioning of the VLEG in the WEC ofFIG. 7B, it will not be repeated except to say that the PMA rotorreaction mass (3) of the basic VLEG in FIG. 9A vibrates in a verticaldirection in response to a vibrational energy source in the same manneras the larger VLEG of the WEC in FIG. 7B.

In FIG. 9G, a structural variant of embodiment one of the VLEG is shownin cross section view where, at the ends of the PMA rotor, an upper anda lower deflecting magnetic field magnet, 212 and 213 respectively, areadded and, in FIG. 9H, a structural variant of embodiment two of theVLEG is shown in cross section view where at the ends of the PMA stator,an upper and a lower deflecting magnetic field magnet, 212 and 213respectively, are added; in both cases, this structural arrangement ismuch more advantageous when the stroke distance of the rotor of eitherembodiment is so long that the end braking magnets 74 and 75 cannotsimultaneously both provide a braking function and an ability to deflectthe magnetic flux lines emanating into and out of the end pole pieces 51and 60 of FIG. 9D of the PMA back into the PMA for increased magneticflux coil linkage at the PMA ends as depicted in FIG. 9D; the magneticdeflection effect of end braking magnets 74 and 75 can only both brakethe PMA and focus the magnetic flux emanating into and out of the endsof the PMA back into the interior of the PMA when the stroke distance isonly a distance of about half the axis length of the VLEG basic PMAstructural unit or less. The use of more powerful magnets with greaterrepelling force extends this distance accordingly. The end magneticdeflecting magnets have a diameter equal to that of the PMA but have athickness that is a fraction of, and in the favored configuration, aquarter of the thickness of the magnets of the PMA that are used toconvert kinetic energy into electrical energy; the magnetic fielddeflecting magnets 212 and 213 do not function with the primary purposeof converting kinetic energy into electrical energy, but rather to bendback and focus the escaping end magnetic field lines toward the PMAinterior poles of opposite polarity thereby reducing flux leakage outinto space and to promote the function of the energy converting magnetsof the PMA. This structural addition to the PMA is advantageous withregards to efficiency of the device by increasing the flux gradientcoming into and out of the sides of the PMA into the regions of spaceoccupied by the coils of the FCA by a considerable amount that has beenmeasured in constructed prototypes. This structural addition may beadded to any VLEG, in the WEC of the present principles, or otherwise inany other type of apparatus in which the VLEG will be used where thestroke distance over which the rotor vibrates is longer than the reachof the magnetic field of the end braking magnets 74 and 75. Inaccordance with the present principles, because of the considerabledistance that the end braking magnets are located from the proximity ofthe PMA, the end magnetic field deflecting magnets are used; for VLEGsused for other sources of vibrational energy with smaller amplitude ofvibration, their function can be performed by the end braking magnets 74and 75 on FIGS. 9A and 9B and 28A and 28B in FIG. 3A.

In general, it is more technically easier to collect and take offelectrical power from an armature containing the power generating coilwindings that is a stator rather than a rotor. One does not have to thendeal with slip or collection rings, commutators, or moving wires thatmay be subject to metal fatigue and breakage. There may be applicationsfor the VLEG where the first embodiment of the PMA rotor-FCA stator VLEGis more advantageous in terms of functional design, cost, or otherfactors; however, there are other applications including those that callfor the use of the largest and most powerful PMA structures by magnetsize, magnet magnetization strength, and number of magnets involvedthough the potential instability of such massive magnetized structuresin vertical oscillatory motion as characterized by a PMA rotor in thepresent principles becomes a limiting factor. Counteracting thislimitation, the kinetic energy imparted to the rotor becomesadvantageously greater in a linear fashion with the mass of the rotor,and in general, the large magnets of large rotor PMA's would tend tohave more mass than FCAs that would be used for the rotor.

While the basic VLEG magnetic unit employs 4 coils in its describedconfiguration, for more practical and efficient wave kinetic energycapture and dissipation into electrical energy, the number of coils thatwould be in a preferred configuration for this function would be atleast 8. As explained above, for maximal results to be obtained for awave vibration of given significant height, the rotor PMA stroke volumeshould be contained within coil windings and should be equal to a lengthof 3 times the axial length of the basic VLEG unit's PMA (a length equalto the significant height of the wave). Thus, 12 coils should preferablybe used. It is clear that in the preferred but not exclusiveconfiguration where the combined width of the 4 coils of the basic VLEGis approximately equal to that of axial length of the PMA, the width ofthese coils will depend on the thickness of the NdFeB or other rareearth magnets used, which also determines the thickness of the polepieces employed in the interior and ends of the PMA.

The Suspension System of the VLEG

Unique to this device are several advantageous characteristics: 1) 3reaction masses—reaction mass (1) includes the fixed subunit and itscomponents including the stator of the VLEG which in turn may beattached to anything from the seabed or any point on land, to any rigidstructure attached to the seabed or any point on land, or to a largevolume water filled heave plate system such as used in the presentprinciples, the Inertial Liquid Wave Dampening System (ILWDS) that ispart of the fixed subunit of the WEC for structures that are not rigidlysecured thereby preventing the stator of the VLEG from movingsignificantly; reaction mass (2) in which a source of kinetic energy cancause this mass represented in the present principles by the floatationcollar of the mobile subunit of the present principles to oscillate in adefined phase relationship to the excitatory source of energy therebycausing the rotor of the VLEG to oscillate and attain significantvelocity; reaction mass (3), which is the mass of the rotor itselfoscillating in the same phase relationship as reaction mass (2), and asit does so, the reaction mass (3) directly converts the kinetic energyinput into electric energy; the ratio of mass between reaction mass (1)and the combined masses of reaction mass (2) and reaction mass (3)should be made as high as possible within the constraints of the designof the WEC or any other energy converting system using a VLEG such as inwave, wind, surf, transportation vehicle and rail traffic vibrationenergy harvesting as representative but not all inclusive sources ofvibratory kinetic energy; 2) a string suspension system comprising: a)an upper perturbing force spring or spring system as shown in FIGS.3B(1) and FIG. 3B(2) respectively of non-corrodible non-magnetic metal,preferably stainless steel, whose spring constant is such to best matchthe mechanical coupling of the energy emanating from the vibratingenergy source during both the positive and negative (but primarily thepositive) sloping half-cycles of the kinetic energy input cycle, usuallybut not necessarily a sine wave; b) a single lower restoring forcesingle spring as shown in FIG. 3A, FIG. 7A, FIG. 7B, FIG. 9A, FIG. 9B,FIG. 9G and FIG. 9H of the same material but of a different springconstant to best match the mechanical coupling of the energy emanatingfrom the vibrating energy source during both the negative and positive(but primarily the negative) sloping half-cycles of the kinetic energyinput cycle. It can be shown that the spring constant of this seriesspring connected mass spring system is equal to K_(p)K_(r)/(K_(p)+K_(r))where K_(p) and K_(r) represent the spring constants of the perturbingforce and restorative force springs respectively. In the preferredconfiguration, K_(p) should be significantly greater (i.e. stiffer) thanK_(r) and both springs should always be under some tension in order toprevent undue vibration and snapping motions of the stainless steelcable from sudden and irregularly shaped waves.

It is believed that the suspension system of the VLEG, which constitutesthe energy dissipating mechanism of the EKS and its repeating unitWEC's, is unique in form and structure. Furthermore, other noveladvantages of this system are:

1) The use of one of the reaction masses, reaction mass (3), to directlyconvert its moving kinetic energy in either the FCA rotor or PMA rotorinto electrical energy rather than redirecting its kinetic energy intorotary wheels and turbines, hydraulic lifts and columns, pulleys,spherical bearings, or gear linkages and other more complicatedmechanical means.2) The use of one reaction mass (1) that is massively larger than thecombined mass of the other two reaction masses (2) and (3) so that evenif the VLEG and any apparatus in which it is incorporated such as theembodiments described herein, the EKS embodiments, is placed in a freelytethered or floating medium such as the ocean, significant relativemotion between the stator on reaction mass (1) and the rotor reactionmass (3) attached to reaction mass (2) will occur.3) The net force acting on the rotor, reaction mass (3), may not beequal on the positive sloped half of the input energy waveform cycle(trough to crest) to the net force acting on the rotor on the negativeslope half cycle (crest to trough) creating unequal velocities of therotor and asymmetric kinetic energy dissipation and electric energyproduction during the entire cycle which is not desirable due toincreased difficulty in regulating the electric energy removed by thePower Collection Circuit (PCC) requiring larger filter capacitors, morecomplex circuitry for load and line regulation. For instance, if thereaction mass (2) input force represented by an asymmetric wave inputforce on the buoy floatation collar mobile subunit in the EKS repeatingunit WEC is much greater than the gravitational weight of reaction mass(3), the rotor containing the PMA or the FCA, the positive upswing,caused by the positive half of the wave being significantly greater inmagnitude than the negative half, a situation more common than the otherway around, for the rotor as the buoy floatation collar is forced upwardby the wave in the trough to crest half cycle could be much moreforceful than the gravitational weight pulling the rotor down on thecrest to trough half cycle causing asymmetric kinetic energy dissipationand electric power generation. This can be balanced out by increasingthe spring constant of the lower restoring force spring but keeping itsignificantly lower, that is, less stiff, than the spring constant ofthe upper perturbing force spring. The spring constants can be adjustedfor the best symmetric pattern for ocean waves that are onlysemi-sinusoidal and asymmetric. For example, the ratio of the springconstant K_(P) of the upper perturbing force spring to the springconstant K_(R) of the lower restoring force spring can be decreased asnecessary while keeping the ratio significantly greater than one. Apreferential range for spring constants would be approximately 0.5 to2.0 pounds per inch for the lower restoring force spring andapproximately 5.0 to 20 pounds per inch for the upper perturbing forcespring, and in the preferred configuration, the ratio of the two springconstants would be approximately 10:1 or less, as such a configurationhas worked well in constructed prototypes.4) During alternate half cycles of the incoming ocean wave, energy canbe stored and released in alternate fashion by first the upper springthen the lower spring. The incident wave may often deviate quitesignificantly from a pure sine wave resulting in highly asymmetricallypositive and negative sloping half cycles. The separate springs andtheir spring constants will more efficiently couple these asymmetricalhalf wave disturbances onto the moving mass (2), the mobile subunit, andthence to mass (3), the rotor, thereby increasing the efficiency of thekinetic energy transfer to the rotor allowing the system to resonate intune with the wave form of the incoming vibratory energy wave, whichgreatly improves the mechanical impedance matching between the incomingenergy wave train and the vibrations of the rotor and improves theefficiency of the kinetic energy capturing and dissipating process, andthereby increases the efficiency of the production of electrical energy.5) Vibratory wave energy sources are often not pure sine waves becausethey may represent complex wave forms due to wave trains summingtogether from separate directions, such as in the case of vibrationscaused by surf crashing along a shore or ocean waves in large bodies ofwater. As a result of this phenomenon, there are often horizontallateral force components and torsional rotating lateral force componentsthat can put stress on the rotor which can only respond to directlyvertical components of the energy wave force input. Hence, springs, ascompared to long axis linear sliding rods, bearing trains, hydraulicsliding columns and like mechanical means, can better dissipate theseunwanted components, greatly improving the operating lifetime of thesystem by reduction of metal fatigue and frictional forces. This rotorspring suspension system is particularly advantageous in damping out thedeleterious horizontal linear and rotational torsional forces within themobile subunit due to wave asymmetry that can develop between thefloating buoy collar and the rotor attached to it. The suspension systempreserves the advantageous vertical linear motion that is desired to bein phase with both the buoy collar and the attached rotor resulting fromthe vertical motion of the instantaneous wave amplitude passing throughthe system. This advantageous characteristic is further enhanced byuniquely arranging the helix direction of the upper perturbing forcespring to be oriented oppositely to the helix direction of the lowerrestoring force spring, thereby allowing for these undesirableperturbing forces on the oscillating rotor to be damped out by theresulting oppositely directed twisting displacement motions and exertedforces of the two springs in response to these undesirable perturbingforces exerted upon them and the cable attached to the PMA.6) To be able to harvest and dissipate vibratory waves of hugemagnitude, such as large ocean waves, the alignment of the rotor and thestator as far as maintaining a proper narrow air gap between them andreducing frictional forces between them should be extremely precise withvery tight tolerances that should be maintained over long periods ofintense vibratory activity. The spring suspension system is much moretolerant of this than linear spherical ball bearing trains, linearsliding rings, and other mechanical arrangements. Also, parasiticdamping forces from these causes can be better and favorably attenuatedwith a mass spring system.7) By allowing the system to resonate at its mechanical resonantfrequency in tune with the frequency of the wave form of the incomingvibratory energy wave, the mechanical impedance matching between theincoming energy wave train and the vibrating rotor is greatly improved,in turn improving the efficiency of the kinetic energy capturing anddissipating process. The efficiency of the production of electricalenergy is increased; the electrical power generated and the quantity ofkinetic energy dissipated is thereby maximized for a given size ofincident wave. Though this can never be accomplished perfectly becauseof non-sinusoidal wave asymmetry and because the fundamental frequencyof the incoming ocean waves will vary with time, since the mechanicalresonant frequency of the system is equal to ω=(K_(pr)/((M2+M3))^(1/2)where ω=the mechanical resonant angular frequency of the mass springsystem, and where M2 represents the mass of the mobile subunit buoyfloatation collar of the WEC, M3 represents the mass of the rotor PMA(neglecting the weight of the attached springs) and K_(pr)=the seriesconnected combined spring constant as previously defined, we can withthis system adjust the stiffness of the springs for a given rotor massto get as close as possible to this resonant frequency match to theincoming waves. While ocean waves are the representative example forexpository purposes, this applies to any form of vibratory wave energysource including those produced by wind, vehicular and rail traffic,crashing surf, ship wakes, and so forth.8) Parasitic damping, which robs a spring-mass VLEG of its efficiency,can lessened in this spring-mass system by favorably utilizing itsunique structure characteristics thereby allowing the stiffening andsuitable adjusting of the spring constants to reduce thermoelasticlosses, by thereby allowing the decreased sliding friction through theuse of special lubricants as described previously as well as allowingthe PMA mass (3) essentially ride a cushion of air comprised of thenarrow air gap between the PMA and the slotted rotor sliding tube, bythereby allowing the decrease in air resistance to the stroke of therotor mass (3) by the favorable features of the VLEG including thehollow central support column, sliding rotor tube slot, and end airvents for hard plastic slotless rotor sliding tubes, and by therebyallowing for minimization of wasteful unwanted vibration in mass (1),the stationary mass, by making the ratio of mass (1) as high as possibleto the sum of mass (2) and mass (3). This allows for a quantity known asthe quality of the spring mass system, Q, analogous to the Q factor in aRLC electrically resonant circuit, to be made as high as possible; ahigher Q factor allows for superior conversion of input vibratory energyinto electrical energy. Since it can be shown that Q is equal to{(K_(pr)*M)^(1/2) D_(p) where K_(pr)=K_(p)*K_(r)/(K_(p)+K_(r)),M=M(2)+M(3), is as defined previously, and D_(p), the parasitic damping,can be measured experimentally by subjecting the system to a singlewave, measuring the S_(r), the resulting rotor stroke distance,measuring ω, the angular wave frequency, (ω=2πf where f is the wavefrequency) by observation or with an oscilloscope, the frequency atwhich the system naturally oscillates at, and knowing F_(in), themeasured force of the incident wave, then D_(p)=−F_(in)/(ωS_(r)). Theserelationships mathematically express the ability to adjustadvantageously the parameters of this particular spring-mass system forthe maximum performance in the manner that was explained, in particularby maximizing the sum of mass (1) plus mass (2), maximizing the ratio ofmass (1) to the sum of mass (1) plus mass (2), by maximizing K_(pr), andby maximizing the ratio of K_(p) to K_(r). The WEC repeatingsubcomponent of the EKS comprising the present principles has aconfiguration of this spring-mass system in its VLEG that allows forsuch optimization.

Compressive Repulsion Magnetic Field Technology

The VLEG uses a very advantageous magnetic pole orientation in thePermanent Magnet Array used either in the rotor or the stator of thefirst or second embodiment of the device. Most technologies in the fieldof electrical power generation use magnets, permanent or electromagneticin type, whose poles are oriented in opposite polarity configuration.The present principles, through the use of the VLEG, employs a magneticpole orientation that is drastically different. In particular, themagnets of the permanent magnetic array can be oriented such that likepoles of the magnets are disposed adjacently to concentrate a magneticfield through the field coil array, as discussed herein below, forexample, with respect to FIG. 5A.

Referring initially to FIG. 4A, two similar magnets in size and magneticstrength have a north pole facing a south pole. This is prior art foundin numerous types of technologies. All the flux flows out the north (N)pole of the left magnet, around in space to the south (S) pole of theright magnet, and then completes the magnetic circuit by flowing throughthe N-S pole interface and back to the original N pole. The forcebetween the magnets is attractive and equal in magnitude to the force ofone of the magnets attracted to a very thick magnetic plate. Most of theflux comes out of the magnet at its ends, very little in the directionperpendicular to the axis of the cylinder formed by the two magnets,whose strength together is twice that of each magnet with twice the fluxleaving and entering the ends as compared to one of the magnets.

FIG. 4B illustrates quite a different magnetic field pattern. Here the Spole of each magnet was brought adjacent to each other causing much lessmagnetic lines of force to come out the ends of the combined magneticcylinder, and many more lines of force to come out perpendicular to axisof the cylinder. For large magnets it requires tremendous force to placethese two like S poles in adjacent opposition to each other andcounteract the extreme repulsive force equal in magnitude to the forceof attraction of one of the magnets alone against a heavy steel plate.Most of the magnetic field lines of the two magnets are squeezedimmensely into a much smaller space resulting in a far more intensemagnetic field in the region of space where copper coils around themagnet would be placed for a generator in accordance with the presentprinciples. This is clearly seen by the array of X's and O's on FIG. 4Aand FIG. 4B which represent the presence of a coil winding; the array ofX's denote the windings of a coil surrounding the magnet pair going intothe paper and the O's denote the windings of that coil coming out of thepaper. The coil windings are clearly located in a region of highermagnetic flux with the S poles in repulsive opposition and it is clearlyseen that the total number of flux lines from the two magnets aresqueezed into a smaller spatial volume leading to an increased fluxdensity. Though the surface pole magnetic flux density, B, that might betypical for a rare earth magnet used in exemplary embodiments of thecurrent invention would be about 5000 to 6000 gauss (0.05 to 0.06Tesla), the compression of the magnetic fields would produce a fieldintensity of twice that exceeding 10,000 gauss or 1.0 Tesla.Measurements have been taken to confirm this field intensification. Itis clear that if the magnet pairs were to vibrate in a linear direction,x, along their axial length, the magnetic flux gradient represented bythe number of flux lines of force being cut by a conductor, that is fluxconductor linkages, dφ/dx, or the flux gradient along the direction ofvibration consists of magnetic flux lines perpendicular to thestationary coils, is far more intense with the repulsive fieldconfiguration than with the standard conventional attractive fieldconfiguration. Hence, for a vibratory motion of the magnets of equalamplitude, velocity, and angular frequency, the power generated in thecoils of FIG. 4B will be quite more significant than for the coils ofFIG. 4A.

FIG. 5A shows the magnetic field distribution of a VLEG PMA embodimentemploying 3 VLEG Magnetic Unit Structures; inset FIG. 5B shows aconventional prior art magnetic field configuration. Each VLEG magneticunit structure as described previously is comprised of 2 NdFeB rareearth magnets plus 2 pole pieces, which together with one additional endpole piece constitutes the basic VLEG PMA magnetic structural unit. Theend magnetic field deflecting magnets may be added as necessary to theVLEG basic magnetic unit structure. A novel and preferred feature of allVLEG PMA structures described herein, is that the structure comprises astack or vertical array of VLEG magnetic unit structures of at least onein number plus one additional end pole piece assembled in thecompressive repulsive magnetic pole configuration. Thus, in an exampleof the preferred embodiment, if y is an integer greater or equal to one,the number of VLEG PMA magnetic unit structures in the PMA is y, thenumber of magnets in the PMA equals 2y, the number of pole pieces equals2y+1, and the number of regions of repulsive magnetic fields where likepoles face each other is 2y−1. This mathematical description forces thetwo end poles of the VLEG PMA to be of the same polarity in completeopposition to the conventional PMA of the prior art described abovewhere magnet stacks in the alternating attractive pole arrangement ofnecessity have one end pole being of opposite polarity to the other endpole.

The total flux emanating from one magnetic N pole and flowing into onemagnetic S pole is designated 1N and 1S respectively. Referring to FIG.5A and FIG. 5B, this flux quantity, 1N (or 1S) designated as 45 and 52respectively, of total flux lines are present at each end of the VLEGPMA structure N (or S) pole; 2N (or 2S) total flux lines designated as49 are present in each repulsive field space along the side of thestructure between adjacent like magnetic poles accounting for thedoubling in magnitude of the B (magnetic) field measurements quotedabove. In actuality, in the specially designed PMA's for the exemplaryVLEG embodiment described here, where there is an additionalspecification that follows from the above numerical rules, namely thatthe end magnetic poles should be always of the same polarity, what ismeasured is that the flux densities B in the outer repulsive fieldregions closer to the end of a long PMA is a bit less than the innermostrepulsive field regions due to the manner that the flux lines emanatingfrom the N pole (or into the S pole) of the PMA cannot go far and widelyinto space and return to the other end pole (as it is of the samepolarity as the pole that they had left) as in the case of theconventional attractive field array described above; instead, they mustreturn to a complementary opposite inner pole, a distinctive furtherbenefit in increasing the flux density in the vicinity of the coilwindings. By contrast, in the prior art of configuration of inset FIG.5B, a total of 4N flux lines and 4S flux lines designated as 41 and 44respectively are present at the N pole and S pole respectively where theflux lines are undesirable, and hardly any flux lines are present in thespace along the sides of the PMA where they should intersect surroundingcoil structures.

Let the x axis represent the longitudinal axis of the PMA parallel tothe direction of vibration of the PMA, and let dN/dx represent the coilturns gradient along the x axis which when integrated over x yields thetotal number of coil turns, N, in the coils surrounding the PMA throughwhich the flux lines intersect. Now let dφ/dx represent the magneticflux gradient along the x axis of the VLEG magnet vibration directionthat enters and leaves the PMA perpendicular to its outer cylindricalsurface; this flux gradient is intensely greater in the repulsive poleconfiguration as compared to the conventional attractive poleconfiguration. Let the flux gradient be integrated over x yielding φrepresenting the total number of flux lines produced by the PMA leavingand re-entering it. From Faraday's Law, the induced voltage (hencecurrent, power, and electrical energy) is proportional to the amount offlux lines cut by a conductor (flux conductor linkages) per unit oftime, and this amount is proportional to the product of both φ and N aswell as the velocity of the PMA during its vibration. This leads to theconclusion that, for a given FCA of given geometry and total coil turnsN, because total flux φ traveling across the cylindrical side of the PMAis a huge number in the repulsive like pole configuration as compared tothe conventional attractive opposite polarity configuration, the amountof power production in the coils would be very large in the formerconfiguration, and very small in the latter configuration.

Because magnetic flux lines around a magnet are always closed loops evenif some appear to extend to infinity, the number of flux lines that comeout of any VLEG PMA structure must always equal the number of flux linesgoing back in; thus, the strength of the fields in the repulsive fieldregions must be twice that at the end regions of the PMA (allowing forthe mild non-uniformity mentioned above), and the total amount of fluxlines generated by the VLEG PMA structure as seen in FIG. 5A isidentically equal to a conventional attractive pole PMA structure asseen in FIG. 5B. It is the radically different configuration andarrangement of the magnetic poles that lead to a radically differentdistribution of the magnetic field lines that constitutes the noveldesign of preferred VLEG PMA structures whether it is only a basic unitas described or large multi-magnetic structural unit PMA structures thathave been built and demonstrated to be of great benefit to the energyconversion function in the WEC repeating component of the EKS. In theinset FIG. 5B for comparison, we see a PMA of conventional prior artwhere the N and S poles are in an alternate pattern resulting in fluxpatterns that are totally different. In prior art conventionalarrangements, very little magnetic flux emanates from the cylindricalside of the PMA, where the FCA is placed in accordance with the presentprinciples, and moreover, what flux that does come out is parallel tothe axis of the PMA cylinder, in a distinctly inefficient andundesirable location and direction, especially for the exemplaryembodiments of the VLEG described herein. Mostly all the flux leaves andre-enters the cylinder at the ends which is the least desirable place toposition the coils as the coils would have to be prohibitively large andcostly to capture a reasonable percentage of the flux stream.Furthermore, many flux lines exiting the end poles parallel or nearlyparallel to the long axis of the PMA cylinder will never intersect acopper coil and hence will be wasted, a phenomenon known as magneticflux leakage. All of these characteristics of the prior artconfiguration of FIG. 5B are undesirable and are eliminated or greatlyimproved upon by the exemplary embodiments described herein. While theseescaping flux lines can be bent toward the end coils using heavyferromagnetic metal armature structures, this was judged undesirable inpreferred embodiments of the present principles because of weightconsiderations and because Compressive Repulsive Magnetic FieldTechnology does away with the need for these heavy armature structuresas will be explained subsequently.

A further very important explanation of the derived benefit and novelfeatures of the preferred examples of VLEG PMA structures describedherein is that the end magnetic poles of the PMA should be in repulsivemagnetic field mode and, as such, should have the same polarity. Thisconfiguration is consistent with the unique and specifically definedmathematically structure given above. In the conventional opposite poleattractive magnetic force PMA, many flux lines starting outperpendicular to the face of one end pole and flowing parallel to theaxis of the cylinder will sweep out huge magnetic flux line loops inspace that are totally useless to cut across coil lines unless hugecoils were placed at and far past the ends of the structure, and still,many flux lines will escape intersecting a coil winding producing severemagnetic flux leakage. In the present configuration, a flux line of oneend pole, no matter how far it will sweep into and around space, cannotreturn to the other end pole of the VLEG PMA structure because it is oflike polarity to the first pole. Hence, that line of magnetic flux mustbe directed to the closest available pole of opposite polarity when itattempts to return to the PMA structure causing it to impact the PMA atan interior point along its length axis where it will intersect thecoils surrounding the PMA. The amount of flux lines that are lostuselessly to huge magnetic loops in space, that is, magnetic leakage, isbeneficially and significantly reduced with the current configuration.

Now if the magnets of FIG. 5B are oriented as per FIG. 5A and are forcedtogether, a great amount of force and expenditure of energy would beneeded to assemble a PMA structure representative of the novel“Compressive Repulsion Magnetic Field” Technology (CRMF). Specifically,the magnets are affixed under a compressive strain due to repulsiveforces resulting from the proximity of like poles. Here, the proximityof the like poles is such that are sufficient to cause the magnets toaccelerate with substantial force in opposing directions if the magnetswere not affixed. This structure is therefore assembled with asignificant expenditure of energy that is stored in a high potentialmagnetic energy state with that energy being stored in the structure'scompressed magnetic fields as opposed to the conventional attractivepole arrangement where potential magnetic energy of the magneticstructure is lowered as it is assembled and energy of the system is onlyincreased when the magnets are pulled apart. Because such a collectionof powerful rare earth magnets with compressed repulsive magnetic fieldsare highly unstable, such a structure containing large amounts ofpotential energy contained within the compressed magnetic fields can flyapart with explosive and harmful force if dropped or mishandled.Furthermore, because of the difficulty in building and maintaining suchan arrangement even for small sized WEC's, such a compressive repulsionmagnetic field PMA should be stabilized using a novel structurecomprising 4 components of the preferred VLEG PMA embodiments describedherein and referred to in FIG. 9A and FIG. 9B: (1) special magnets 37 aand 37 b that have an inner cavity 47 through which (2) a stainlesssteel support tube 36 runs with (3) pole pieces 51, 53, 54 that separatethe magnets all bonded together by (4) a very strong magnetic epoxy (notvisible) as exemplified but not exclusively represented by JB Weld® witha holding power of at least 3,500 pounds per square inch that was usedin constructed prototypes. The repulsive force between a given pair ofadjacent magnets in a PMA is significant and is sufficient to cause themagnets to accelerate in opposing directions if the magnets were notaffixed. Indeed, this structure converts a very hazardous and unstablemagnetic configuration, essentially a “magnetic stick of dynamite,” intoa stable one that produces multiple regions of compressed magnetic linesof force with magnetic field intensities that are much increased inmagnitude in the regions of space where the copper field coils will beplaced thereby greatly facilitating the production of electrical energy.Hence magnetic fields are focused, directed, and amplified in theregions of the electric power generating coils without the heavyarmatures used for such purposes with attractive magnetic poleconfigurations. Hysteresis and eddy current losses are significantlyreduced and the magnetic drag by the magnets of the rotor as they movein the vicinity of a heavy ferromagnetic armature are eliminatedalthough the Lenz's law back EMF force on the rotor due to the coil'sinduced current remains.

It should be noted that the method of fixation of the magnets and polepieces together was accomplished with the strongest of magnetic epoxies.However, as discussed in more detail herein below, the fixation of themagnets together can be implemented by mechanical compression andfixation by means of pole pieces with a threaded central hole attachedto the rare earth magnets with a central non-threaded hole which is thenthreaded as a unit onto a central structural tube that is also threaded,and in this case, the central support tube can be non-magnetic stainlesssteel, brass, and other non-magnetic materials. Here, the threadsfacilitate the assembly of such powerful magnets in a controlled manner.

The repulsive force distributed along the long axis of the PMA can existover a huge range. Using the most miniscule magnets (⅛″ o.d.× 1/16″i.d.× 1/16″ thick N42 magnets with a pull of 0.36 pounds), a 6 magnetPMA with 7 pole pieces (excluding the end deflecting magnetic fieldmagnets) would have a repulsive force of 5×0.36=1.8 pounds distributedacross its ⅜″ length with no pole pieces (4.8 pounds per inch). For themagnets used in prototypes of the present principles, the N42 magnetswere 2″ o.d.×0.25″ i.d.×1″ thick magnets with a pull strength of205×6=1230 pounds of repulsive force distributed over a PMA length of9.5″ including 0.5″ thick pole pieces (129.5 pounds per inch). Thelargest N42 magnets available with a central hole are 4″ o.d.×0.25″i.d.×3″ thick with a pull strength of 1200 pounds leads to a repulsiveforce of 5×1200=7200 pounds distributed over its length of 28″ including0.5″ thick pole pieces (349 pounds per inch). Thus, the repulsive forcetending to pull the PMA apart if not for the central anchoringsupporting rod increases dramatically with the size and strength of themagnets, and changes inversely with the thickness of the pole pieces. Byusing magnets of N52 magnetization, these numbers are increased byapproximately 25%. Using thinner pole pieces would of course make therepulsive force per inch of PMA length greater.

In accordance with preferred embodiments, the ranges of the repulsiveforce between a given pair of magnets in a PMA can be tailored andselected based on the particular environment in which the VLEG isimplemented. For example, 20 to 100 pounds of repulsive force between agiven pair of magnets in a PMA can be employed for bodies of water thatare calm with relatively small waves, such as inland seas and largelakes. Alternatively, this range can be employed for WEC embodiments inwhich WEC's multiple PMA higher order VLEG electrokinetic matrixtransducers are used and incorporated. Further, 100 to 300 pounds ofrepulsive force between a given pair of magnets in a PMA can be employedin oceans of more typical waves of larger and more typical size. Inaddition, the 100-300 pound range can be employed in PMA VLEGElectrokinetic Matrix Transducers that are relatively few in number. Forexample, for environments to which the 100-300 pound range ispreferentially directed, WEC's can contain one to a small number ofPMA's in their VLEG Electrokinetic Transducers. In accordance withanother exemplary aspect, 300 to 1200 pounds of repulsive force betweena given pair of magnets in a PMA can be employed in the largest WEC'sdesigned for the largest ocean waves that regularly might occur, such asin the Pacific ocean along the coasts of Hawaii, California and Chile inwhich the WEC can use a single massive PMA in its VLEG ElectrokineticMatrix Transducer. Although a pull strength of 300 pounds to 1200 poundsfor each magnetic pair interface would be most preferential, largercustom-made magnets subject to some potentially limiting factorsdescribed herein below can be employed. It is also to be noted that theair gap factor that undesirably decreases the density of and totalnumber of flux coil wire linkages in the vicinity of the inner portionsof the coils, which occurs with increasing air gap width, becomes lessof a factor as the size and magnetization of the magnets increase for agiven gap width.

While there are no theoretical limits as to how large custom mademagnets can be built, resulting in no limits on the pull strength ofsuch magnets that are used in an WEC, such a limit may be imposed by thefollowing factors: 1) The structural strength of the central supporttube which can be made quite significant; 2) The method of fixation ofthe magnets and pole pieces together, which in embodiments of thepresent principles was accomplished with the strongest of magneticepoxies but may also be done by mechanical compression and fixation ofsuitable and novel means described below; 3) The ability to safelyhandle such large magnets; 4) The spacing between adjacent WEC repeatingsubcomponents needed to prevent undesirable magnetic interactionsbetween the adjacent PMA's of adjacent WEC's should not be so great thatthe wave kinetic dissipation function of the EKS is seriously degraded,as to be explained subsequently; 5) If a VLEG electrokinetic matrixtransducer has greater than one PMA and VLEG, the magnetic interactionbetween adjacent PMA's will very quickly become unacceptably strong asthe size and strength of the magnets are increased; 6) The costs mayquickly become prohibitive with arbitrarily large and powerful rareearth magnets. Likewise, there should be a limitation regarding theminimum repulsive force suitable for the wave kinetic energy dissipationand conversion function of an EKS, which should employ rare earthmagnets of at least a pull strength of 20 pounds, as noted above. Thisthreshold is based upon the fact that magnets of lesser strength wouldsimply not have sufficient quantities of magnetic flux when used in thecompressive repulsion magnetic field technology to produce a largeconversion of wave kinetic energy into electrical power, renderingdevices with less repulsive force relatively inefficient, especiallywith regard to EKS embodiments that rely on the conversion to dissipatepotentially harmful waves. In general, the desirable magnetic pullstrength of individual magnets can fall into being appropriate for threeaspects of the wave kinetic energy dissipation function, as noted above.

With respect to considerations described above that may have impact onlimiting the size and strength of the rare earth magnets used in thePMA, FIG. 5C illustrates the novel means that have been formulated andconstructed to greatly increase the allowable size of such magnets andto greatly facilitate the assembly of such PMA that are subject to suchintense gradients of severe repulsive magnetic force. As compared toFIG. 5A, FIG. 5C shows a compressive repulsive magnetic field PMA, upperend pole piece 54, three interior pole pieces 53 and a lower end polepiece 51, all of which now have a much larger central hole 47 whose sizeis proportional to the size of PMA rare earth magnets 48 and whose sizemay exceed as much as 3 inches or more in diameter. Central hole 47 ofthe pole pieces has a new characteristic of being threaded on itsinterior diameter surface by threads 57B. The configuration of FIG. 5Calso includes a significantly larger diameter central support tube 46whose diameter is just slightly less than the central hole 47 in whichit is contained and that now has a new characteristic of being threadedon its outside surface over its entire lengths by threads 57A that arecomplimentary to threads 57B on the interior inside diameter surface ofpole pieces. In addition, the configuration further includes foursignificantly large rare earth magnets in compressive repulsive magneticfield configuration with a similar sized central hole 47 but whoseinside diameter interior surface is not threaded. Note that the firstPMA prototypes were assembled by hand by exerting considerable handpressure as each new pole piece and magnet, one by one, were compresseddown upon the central support tube 46, suitably immobilized andsubsequently bonded together and bonded to the central support tube'soutside surface with magnetic epoxy as previously described at surfaces57C; the hand compression limited the size and strength of the magnetsused in these prototypes. However, in the modified configuration of FIG.5C, a magnet is bonded to a pole piece and this magnet-pole piece unitis threaded down the central support tube onto its previously placedpredecessor whose upper surface has had a layer of bonding epoxy appliedto it. In this manner, PMA structures of large diameter and length withvery powerful magnets can be assembled in a highly stable, controllable,and safe manner. Essentially, the PMA takes on the structure of a largethreaded screw mechanism which allows precise control of very heavyrepulsive magnetic forces. Because of this controllability factorcreated by threads 57A on the central support tube and threads 57B onthe pole pieces, in addition to the central support tube being composedof nonmagnetic metals such as stainless steel or brass, the tube may nowbe composed of magnetic materials without increasing the instability ofassembly and also allowing for better focusing of the magnetic fields inthe areas of repulsive magnetic regions. Furthermore, this novel meansof construction and assembly of the PMA allows for thinner pole piecesand higher magnet thickness to pole piece thickness ratios, therebysignificantly increasing the intensity of the repulsive magnetic fieldsin between the magnetic pole pieces, which offers the followingadditional advantages that result in increased wave kinetic energy powerdissipation and more byproduct electrical energy being produced: 1) Moremagnetic flux linkages through the FCA coils; and 2) a shorterlongitudinal axial length of the PMA. The smaller resulting weight ofthe pole pieces allows for either thicker more powerful magnets or moremagnets of the same strength to be used within the same PMA volume ofspace.

Note that in embodiments of the present principles, cylindrical magnetswere used. However, magnets of any geometrical cross section that aremagnetized preferentially in their thickness dimension can be usedshould special applications require it.

Theoretically, the repulsive field pole pieces or coupling elements 53of FIG. 9A and FIG. 9B could be dispensed with as per FIG. 4B. However,there are two distinct advantages having these pole pieces in place: 1)the stability of the structure is greatly improved as far as the ease ofassembly—for example, to ease assembly in the working prototypes, eachmagnet and pole piece were successively and individually bonded to thestainless steel tube backbone while under great pressure; the presenceof pole pieces reduces considerably the compressive forces on themagnets needed to overcome their mutual repulsive forces during assemblyas would be evident from the calculations above; 2) more importantly,since the pole pieces are made of suitable highly ferromagneticmaterials such as low carbon steel, low carbon high silicon electrictransformer steel, and the like, the very high magnetic permeability andmagnetic saturation levels of these pole pieces allow for concentrationand amplification of the total amount of magnetic flux emanating andentering the PMA where the coils reside so that the regions ofcompressed magnetic fields have still higher field densities; the polepieces act like magnetic windows and lenses that concentrate and directthe magnetic flux out and into the PMA perpendicularly to its long axisdirectly through the encircling FCA windings greatly increasing fluxcoil winding linkages, again without the use of heavy coil surroundingarmature structures. Essentially the repulsive pole pieces of the PMAperform the same focusing and magnetic field intensity amplificationfunction as heavy ferromagnetic structures in the stator with thepreviously mentioned disadvantages, and in effect, the focusing andmagnetic field intensity amplification functions are located on the PMArotor themselves rather than on the stator. This particular advantageouscharacteristic is more apparent and significant on the preferred firstembodiment of the VLEG with the PMA rotor and the FCA stator althoughthe advantage also exists with the second embodiment of the PMA beingthe stator and the FCA being the rotor. Ideally, the higher the ratio ofthe magnet thickness to the pole piece thickness, the more magneticfield compression and concentration one has, the more electric power isproduced, and the less amount of copper with smaller and less costlycoil windings that can be used. However, if the thickness of therepulsive pole piece becomes too small relative to the magnet thicknessand diameter, aside from the PMA becoming very difficult to assemblewhen dealing with large magnets because of the tremendous compressiveforces and energy needed and the theoretical possibility of structuralfailure with the magnets and pole pieces flying apart at high velocity,the pole pieces will reach the magnetic saturation point (for hard lowcarbon or electric transformer steel, about 18 KGauss or 1.8 Tesla) sothat the pole piece will become less able to contain and focus themagnetic repulsive field onto the coils in the effective manner justdescribed. The preferred range is estimated to be a ratio of magnetthickness to repulsive pole piece of 2:1 to 8:1. In fact when the ratiois properly adjusted for the given sized magnet of a given strength ofmagnetization as it has been in the presently described embodiments ofthe VLEG used in the WEC repeating component of the EKS apparatus sothat virtually all of the magnetic flux can be encompassed within andcompressed into the repulsive pole piece to be directed out across theencircling coil windings, another favorable operative feature of therepulsive pole piece emerges. While a large compressive force has to beexerted in assembling each magnet in the repulsive field mode onto themagnet stack, when that magnet just approaches the pole piece of correctthickness that is over the magnet underneath, the new magnet being addedsuddenly is weakly attracted to the pole piece because of magneticinduction on the upper surface of the pole piece; the inter-magnet forcesuddenly becomes weakly attractive, and the force adds to the stabilityof the PMA because that PMA is in a lower energy state than when theadditional magnet is a slightly greater distance away. The repulsivepole piece may be either a solid cylinder, or if especially siliconelectric transformer steel is used, the pole piece could be built up aslaminated layers bonded with suitable magnetic high strength epoxy. Theadvantage of the latter arrangement is that eddy losses from Lenz's LawBack EMF current generation in the pole pieces which could slow down therotor PMA's velocity are reduced. However, the very strong internalrepulsive magnetic forces within the pole piece should be taken intoconsideration with respect to the stability of the PMA structure; forsmall magnet structures, bonded laminated cylindrical pole pieces areadvantageous in some applications, but for larger magnet structures, thesolid much stronger cylinder pole pieces would be the preferredembodiment. Note that the geometry of the pole pieces may take shapesother than a cylinder, but the shape taken should match the crosssectional geometry of the magnets being separated by the pole pieces.

There are four additional advantageous operational characteristics thatrelate to efficiency of power generation that are a consequential resultof the use of pole pieces to direct the flux lines flowing in and out ofthe cylindrical side of the VLEG PMA to encompass the coil windings: 1)there is no magnetic drag on the motion of the PMA relative to the coilwindings caused by the pole pieces themselves being attracted to themagnetic fields of the magnets as in the case of heavy largeferromagnetic armatures surrounding the coil windings; 2) the polepieces do not contribute any undesirable Lenz's Law back EMF forceopposing the relative motion of the PMA with the FCA windings as nocurrents are induced in the pole pieces as opposed to the situationwhereby coil encompassing ferromagnetic armature structures, even withthe use of laminations and appropriate types of steel, have eddycurrents induced within them that contribute to back EMF forceproduction; 3) The only currents that are induced causing an unavoidableproduction of EMF back force inherent to all electrical generators is inthe coil windings themselves and not in the pole pieces; 4) theelimination of coil winding encompassing ferromagnetic armaturestructures eliminates the wastage of energy from hysteresis and eddycurrent ohmic losses that are still present even with the use ofsuitable steels and laminations.

The pole pieces can be clad in a thin ring 38 of non-magnetic stainlesssteel that will act as a sliding bearing with lubrication against theinner surface of slotted rotor sliding tube 32 as shown in FIG. 3A. Inaddition to reducing sliding frictional energy losses, because thesebearing surfaces will make the diameter of the pole pieces slightlylarger than that of that of the cylindrical magnets comprising the PMA,the magnets themselves will not be damaged due to the constant frictionwith the sliding tube. The stainless steel rings may also be applied tothe cylindrical sides of the magnets themselves accomplishing the samebenefit. With either placement, the stainless steel rings also ensurethat the air gap (61 on FIGS. 9A and 9B) between the PMA's cylindricalsurface and the inside of the slotted rotor sliding tube 32 remainsconstant as the rotor vertically slides up and down within the slidingtube, a very desirable characteristic that makes the power generationmore uniform, the sliding motion more uniform, and a decrease in erosivefrictional damage to the inner surface of the tube or the relativelyfragile metal coat of the rare earth magnets used. Note that if themetal coating, usually of nickel or nickel layered with copper, iscompromised due to frictional losses of the rotor against the slidingtube, the NIB (Neodymium Iron Boron or NdFeB) rare earth magnets used asthe preferred embodiment will suffer catastrophic damage—the magnetmaterial structure is brittle and will crumble from mechanical stress,the iron will oxidize increasing magnet brittleness, and themagnetization of the of the magnet will decrease with time as themagnetic metal coating acts as a “keeper” partially short circuitingsome of the magnetic flux from the N pole to the S pole when the magnetis not adjacent to ferromagnetic materials or magnets of oppositepolarity. Additionally, as a result of these lessened frictional losses,the parasitic damping factor associated with the VLEG goes down,maximizing the electrical power generated for a given amplitude of wavevibration.

The advantages of Compressed Repulsive Magnetic Field Technologyinclude: 1) Most of the magnetic lines of force leave and enter throughthe sides of the PMA across the surrounding FCA windings rather than theends of the PMA with the repulsive pole pieces acting as both windowsand magnifying magnetic lenses that direct all of the flux linesdirectly into the FCA coil windings; 2) In the standard attractive polemagnetic field configuration, virtually all the magnetic lines of forceleave the N pole end of the PMA and are distributed over a much largerarea of space before returning to the S pole end thus requiring verylarge coils at either end that must be moved considerable distances tointersect most of the field lines entering and leaving the PMA; 3) Whilethe total magnetic flux lines of force is the same in bothconfigurations, in the configuration of preferred embodiments themagnetic flux lines are concentrated into a smaller area of spaceleading to a more intense magnetic field in the region of the FCA, andin the areas nearby to the repulsive pairs of poles where most of thecoil windings are located; the fields may be as much as 100% moreintense as is clearly shown by the flux field lines produced with thetechnique of fine element series magnetic field imaging in FIG. 4B ascompared to FIG. 4A; 4) In the standard configuration, much of the coilwindings do not produce appreciable power when they are over the regionof the PMA not near the end poles where the efflux and influx of fieldlines occur whereas in the configuration of preferred exemplaryembodiments of the present principles, all magnets of the PMA are alwayssurrounded by the coil windings that are always intersecting significantamounts of flux producing electrical power whenever the coils are overthe PMA except at the crest and trough of the wave when the rotor isstopped; 5) It is much more simple to move a stack of smaller coilsrapidly and for much greater distances then a very large coil at eitherend of a PMA with the standard attractive pole configuration; 6) Themultiple PMA multiple FCA VLEG Electrokinetic Matrix, an advantageousarrangement of multiple VLEG structures to be described subsequently,can simply not be built with the standard configuration and whereas theycan be built using Compressive Repulsive Magnetic Field technology; 7)To prevent a large amount of magnetic flux leakage into space withoutintersection with field coils the standard configuration of attractivepoles requires large heavy ferromagnetic armatures to focus the magneticfield onto the coils—while this is quite characteristic of motors androtor generators, is highly undesirable for linear electric generatorsof this type because of significant eddy and hysteresis losses, therequirement of much more massive dampening systems, the significantincreases in magnetic drag on the rotor, and significant increases inback EMF forces retarding the acceleration and velocity of the rotor.

Note that with regard to focusing magnetic field lines, implementingmagnet stacks in one enclosure shell and the field coil array in aseparate enclosure shell, where one enclosure's side is adjacent to theother enclosure's side, along with an armature is a substantially lessefficient system because of an asymmetric focusing of the magnetic linesof force into the adjacent coil and ferromagnetic armature on one sideof the magnet stack leaving the field lines from the other side of themagnet stack not having penetrated the field windings as well as anecessary increase in the air gap between the magnets and windings ofsuch an arrangement. In contrast, the configuration of magnets inaccordance with CRMF focuses the magnetic lines of force by using thepositions of the magnetic poles themselves instead of heavyferromagnetic armature structures to focus magnetic field lines.Further, in preferred VLEG embodiments, the FCA coil windings completelyencircle the circumference of the PMA to maximize intersection withmagnetic field lines.

It should be further noted that there is virtually no limit to the sizeof the coils and magnets that can be used in the Compressive RepulsiveMagnetic Field configuration as long as the system can accommodate theintense force required to compress large and powerful magnets togetherin a magnet stack. Furthermore, if magnetic strength is defined aseither the degree to which the material composing the magnet ismagnetized, a quantity known as the N factor or magnetic energy productthat ranges from N1 (1 MEGAGAUSS-OERSTED, BH_(MAX)=1 MGOe) being theleast magnetized to a maximum of about N52 (BH_(MAX)=52 MGOe) being themost magnetized, or the pulling force in pounds or Newtons, which isproportional for a given degree of magnetization to the dimensions andvolume of the magnet, the size of the associated coils and the amount ofcopper used is minimized with favorable cost considerations withCompressive Repulsive Magnetic Field technology. It is important to notethat by compressing the repelling magnetic poles closer together withthinner repulsive pole pieces, the length of the PMA can be reduced forany given size magnet being used which beneficially causes the followingadvantages: 1) smaller less costly coil sizes and less copper to be usedfor any given desired power output; 2) the smaller in thickness therepulsive pole pieces are and the closer the repulsive poles are, thesmaller the mass of the PMA rotor will be which allows it to travel at ahigher velocity for a given magnitude of wave force increasing theelectrical power generation and efficiency of wave energy dissipation aswell as allowing the rotor to be braked more easily when necessary for avery large wave by the braking mechanism of the VLEG. The preferredembodiments of the VLEG described here use a structure and configurationof magnets that is distinctly different and possesses advantageouscharacteristics as to enhancing its effectiveness with respect to knownsystems of linear electric generators. The advantages are especiallyapparent with regard to the generation of useful electrical energy bydissipating undesirable ocean wave energy via the wave energy converter(WEC) repeating component described above.

Not only does compressive repulsive magnetic field technology representa significant improvement to the art of electric power generation bymoving magnetic field coil interactions, it is also important to theoperation of the purely magnetic component of the exemplaryelectromagnetic and mechanical breaking system embodiment of the WEC andVLEG described herein. CRMF also is important to the operation of theend magnetic field deflecting magnets in the WEC and VLEG embodimentsdescribed herein. These two aspects of the technology will be discussedin more detail shortly below.

Variable Wire Gauge Field Coil Array

Referring to FIG. 6, shown in magnified detail are the coil windingsthat constitute the FCA of a preferred embodiment. FCA 34 is shownsupported by slotted rotor slide tube 32 separated by air gap 61 fromPMA 37 comprising two VLEG magnetic structure units with end N polepieces 51 and 54, 3 repulsive magnetic field regions with pole pieces,one of which is designated 53. FCA 34 is divided into two layers, aninner small gauge wire layer 55 with a denser wire turns per inch ofhigher resistance wire surrounded by outer coil layer 56 containing alarger gauge wire of lower resistance and a lower density of wire turnsper inch. Thus, a conducting wire of an outer portion of the FCA canhave a thickness that is greater than a thickness of a conducting wirein an inner portion of the FCA closer to the PMA than the outer portion.In this bi-layer variable gauge winding approach, the two differentthickness wires are wired together in series so that their individuallydeveloped EMF is additive in magnitude is a distinguishing arrangementfor wiring armatures in LEGs. The spacing between the groups of windingsis exaggerated for the purpose of illustrative clarity.

Many competing factors go into wire gauge size selection for LEG coils.Coil windings using large wire diameters (low gauge number wires) havethe advantages of less resistance, can carry larger current loads withless ohmic heating loss, are advantageous in keeping the armatureresistance low for certain applications, and stronger wire windings aremore resistant to the Lorentz forces tending to stress apart the coilwindings. However, in these coils the more heavier currents in the wirewindings cause more severe Lorentz force stress than lower currents,more Lenz's Law losses via more production of counter EMF which worksagainst the motion of the rotor, uses a great quantity of copperaffecting undesirably the weight, volume, and cost of the coils, causeincrease eddy and hysteresis losses in metal structures nearby, and havea lower density of turns per inch decreasing the developed voltage inthe coils. Small diameter wires (high gauge wires) have directly all ofthe opposite attributes. Because these many factors often oppose eachother, a compromise should be reached with the final wire sizeselection.

If we characterize the magnetic field around the PMA as having tworegions, a high intensity field area with a high flux density, B, and aregion farther out as the magnetic field falls away with distance fromthe magnet that is of lower flux density, we note that in an area ofhigh flux density it would be advantageous to use small diameter wire tocompose the coil windings near the magnet structure. Such a coil wouldhave an increased number of turns, a higher induced voltage, a decreasewinding to magnet air gap (the distance between a coil winding turn andthe magnet structure), decreased current, increased resistance per unitlength of wire, decreased I squared R losses, decreased coil turncircumference and cross-sectional area, and less back EMF from Lenz'sLaw produced. In the area farther out from the magnet structure in thearea of weaker magnetic flux, it would be advantageous to use largerdiameter wire to compose the coil windings. Such a coil there would havea decreased number of turns, a lower induced voltage, an increasedwinding to magnet air gap, an increased induced current, increased Isquared R losses from the increased circumference of each winding offsetby a decreased resistance per unit length of wire, increased coilwinding turn cross-sectional area offsetting the decreased magneticfield intensity, and again back EMF would be increased secondary toincreased current but the opposing force on the inducing magnet would bedecreased secondary to the greater air gap. If one winding of a constantthickness wire was wound extending from the area of strong to the areaof weak magnetic fields, there would be less optimum conditions due toone of these parameters being favorable in one region of the magneticfield and less favorable in the other. If, however, there are two coilswound on top of the other such that the thinner gauge wire was wound onthe inner portion of the coil close to the magnet structure, and thethicker gauge wire was wound on the outer portion of the coil fartherout from the magnet structure, where the two coils would be connected inseries, we would match the desirable characteristics of the particularwire with the field strength around the coil.

An important aspect of the present principles is the efficiency of thedissipation of ocean wave kinetic energy into electrical energy. Whilethe spring suspension system is important in coupling the kinetic energyof the wave into the kinetic energy of the rotor PMA dissipating thatenergy, the efficiency of the Faraday induction of that rotor kineticenergy into electrical energy is dependent on the strength anddistribution of the magnetic fields resulting in a zone of intersectionof the magnetic flux lines with the field coil array. Optimizing thedesign of the coil by varying the gauge of the wire along the coilwinding has been shown to increase the intensity of the developedmagnetic field of an electromagnet with a coil with a known currentlevel and geometry by 50% as compared to a similar coil of constant wirethickness with superior and more uniform heat dissipation along theentire coil. Using that fact in reverse has lead to the incorporation ofa similar coil variable gauge wire arrangement in the FCA of the VLEG toincrease the amount of electrical power produced for a given geometryand size for the given rotor PMA and stator FCA. By having thinner wireused in the regions of maximum magnetic flux density adjacent to thecircumferential side of the PMA, a large voltage can be developed with asmall amount of copper metal in a relatively small volume and thecurrent can be kept reasonably low throughout the coil to minimize LenzLaw EMF forces close to the PMA where it would produce the most negativeeffect on the latter's relative motion to the FCA; eddy losses in theslotted metal rotor sliding support tube as the rotor slid by the coilwindings would be reduced, and the Lorenz Force on the coil windingswould be reduced where it would normally be most stressing to the wire.The coil wiring configuration in the inner layer would satisfy thecharacteristic of a high voltage and low current situation frequentlydesired in electric machines such as motors and generators. This is veryadvantageous since the power dissipation, P=I²R, increases with thesquare of the current but only increases approximately linearly with thenumber of windings; the power lost in the windings can be minimized byreducing I and increasing the number of turns N proportionally. Forexample, halving I and doubling N halves the power loss. This is onereason most electromagnets have windings with many turns of thinnergauge wire.

However, further away from the rotor, where the flux density issignificantly less, the length of each wire turn should be significantlygreater to generate useful voltage. Furthermore, each outer turn shouldbe laid down on its previously inner adjacent one, so that the turns ofwire have a gradually increasing radius and length. The resistance ofthe wire if the wire diameter was kept small and constant at the samegauge as the inner windings would become prohibitively too high withintolerable energy loss through I²R ohmic losses. The advantage of moreturns producing more voltage will be nullified by the rapidly increasingresistance of the wire as the coil turn radius increases. Also thin wirewould be more subjective to fatigue and failure because of Lorentzforces within the coil at these large radii. To overcome these problems,thicker wire of a lower gauge is used in the outer layers of the coilwhile a thinner wire of higher gauge is used in the inner layers of thecoil. In effect this distribution of windings, rather than trying tocompromise on a wire thickness that would be most suitable to both thehigh magnetic flux and low magnetic flux regions within the geometry ofthe coils, uses a thicker lower gauge wire more suitable for the lowermagnetic flux regions and a thinner higher gauge wire more suitable forthe higher magnetic flux regions in the appropriate areas for maximalpower generation. Other advantages are that heat generation in the coilwill be more uniform and more easily eliminated rather than beingconcentrated in the inner coil windings; current in the entire coil willbe neither too high or too low since a coil with part of its windingwith low thickness wire and part with high thickness wire would have thecharacteristics of a uniform coil with moderate thickness. Furthermore,the undesirable Lenz's Law back EMF would be decreased in both halves ofthe coil in this arrangement because the inner high gauge wire coil isin series with the outer low gauge wire coil, and thus limits theinduced current through the entire coil; because ohmic I squared Rlosses is proportional to the square of the induced current, and backEMF is proportional to the induced current, both of these two sources ofundesirable energy loss will be minimized.

It should be noted that coils of an FCA can be wound to havecontinuously variable gauge thicknesses or several thickness wires usedin series. With this coil configuration, the electrical power generatedper turn of coil winding is more uniform throughout the coil geometry.Because of the numerous factors described here in coil design competeagainst each other, the precise optimal ratio of how much of the coilshould be constituted as the inner thin wire portion and how much of thecoil should constitute the outer thick wire portion would depend on thespecific application and design in which the coil is employed. However,this unique configuration can include a continuously varying gauge wirewinding configuration should prove effective in improving the efficiencyof conversion to electrical power. One must note, however, that it canbe shown that the most optimal partition between thin and thick wire forthe inner and outer section of the coil, and for that matter even with acontinuously variable wire gauge coil that uses progressively lowergauge thicker wire as the coil turns are wound more distant, cannotdecrease the energy losses in the coil by less than a quantity that isproportional to the square of the strength of the magnetic fieldintensity, B. One must note that it is also possible to have additionallayers of varying intermediate gauge thickness copper wire windingsbetween the outer and inner layers just described all connected inseries together as one coil which would be expected to improve upon thetwo layer coil configuration and approximate the continuously varyingwire gauge configuration.

Regarding coil size, in general, the larger the diameter of the magnets,the greater the outside and inside diameter that should be used for thecoil in the FCA. Because magnetic strength and total flux producedincreases with the increase in diameter and magnet volume, the coils canbe wound to a greater useable outside diameter because of the greatervolume of the magnetic field of useable strength. Also, the width ofeach coil depends upon the magnet thickness, as it has already beenmentioned that the preferred range of coil width should be such that thecombined width of the four coils assigned to each VLEG PMA magneticstructural unit be approximately equal to the length of that structuralmagnetic unit to minimize and avoid excessive field line cancellationcaused by the same coil moving over oppositely directed field lines.Finally, in the situation where FCA's are intermingled with PMA's in aVibrational Energy Electrokinetic Transducer Matrix, if the thickness ofthe coil is defined as the difference between its outside and insidediameters, then the combined thicknesses of two adjacent FCA's enclosingtwo adjacent PMA's should be a certain minimum amount to keep the twoPMA's a certain minimum distance from each other to avoid excessiveattractive drag and frictional losses from their mutual attraction oftheir complementary poles which would degrade the performance of thesliding PMA's within their rotor sliding tubes; if this inter-PMAdistance is too short, the PMA's might at the worst simply stop slidingin response to wave action or at best simply wear out the movingsurfaces from friction; if this inter-PMA distance is too long due tothe thicknesses of the coils being too high, the lines of forcetraveling between adjacent PMA's will defocus and undesirably spread outin space. For a VLEG with a single PMA and FCA, to produce a useableamount of power in a coil turn, the coils should be wound to a thicknessno larger than an amount such that their outermost turns lie in amagnetic field intensity no less than 500 to 1000 Gauss (0.05 to 0.1Tesla). In the prototypes constructed where N42 cylindrical magnets ofdimensions of 2″ o.d.×0.25″ i.d.×1″ thickness with 200 pounds ofmagnetic pull were used, this allowed an optimal coil thicknessdetermined by magnetic field strength measurements around the PMA to beapproximately 1.5″. For the Vibrational Energy Electrokinetic TransducerMatrix composed of multiple PMA's in close proximity to each other usingmagnets of this size, the minimum distance of separation betweenadjacent PMA's becomes twice that of the coil thickness just specifiedabove, or 3.0″ representing the distance across the thicknesses of twoadjacent FCA coils surrounding two adjacent PMA's. It is easily seenthat larger or smaller magnets as well as magnets with different crosssectional geometries, such as square and rectangular, or different Nmagnetization strengths would call for coils with thicknesses ofdifferent magnitudes. Furthermore, the use of end magnetic fielddeflecting magnets 212 and 213 illustrated in FIG. 3A, FIG. 9G, and FIG.9H on each PMA has been measured to increase the intensity of themagnetic field around each PMA by 20%. This aspect will allow theoptimal maximum coil thickness to be increased further by approximatelythis amount. As another example, if magnets in the PMA's were of thelowest possible useable strength that, as mentioned previously, shouldbe 20 pounds of pull, magnets of similar shape to that specified in theprototypes but whose volume would be 10% that of the larger magnets(magnetic pull is proportional to volume of magnet magnetic materialcomprising that magnet for a given strength of magnetization) wouldresult in a minimum distance of separation of twice the thickness ofeach coil of 0.7″ or 1.4″ scaling all dimensions down by a factor equalto the cube root of 10, or 2.15 approximately. This arrangement will befurther elaborated on with the detailed structural description of theVibrational Energy Electrokinetic Matrix Transducer herein below.

Another important factor of coil design is the relationship of theeffective resistance of all of the coils in the FCA, i.e. thegenerator's internal resistance, to the load resistance presented to thegenerator's outputs. This is extremely complicated and in the simplifiedcase, one can state the maximum power theorem puts a maximum limit onthe percentage of the electrical power generated that can be transferredto the load at 50% when the load resistance is equal to the internalgenerator coil resistance. However, there is a quantity inherent in allLEG's called electromagnetic damping that should be adjusted carefullyto achieve the maximum electric power generation from a given amount ofinput kinetic wave energy at which the 50% maximum would be applied. Thespring mass VLEG is most efficient when its natural mechanical resonantsystem approximates as closely as possible to the vibrational frequencyof the input energy. Under this condition, the electromagnetic dampingfactor should be equal to the parasitic damping factor. The parasiticdamping factor depends on mechanical and frictional losses in thegenerator as previously described. The electromagnetic damping factordepends on the square of the flux gradient along the moving axis of thePMA, dφ/dx, as previously described, and this quantity is set by the PMAgeometry and magnet strength and size. It also depends on the square ofthe number of wire turns in the coil. Finally, it depends on the sum ofthe coil resistance and the load resistance of the generator.

It can be shown that when the frequency of the wave is as close aspossible to the mechanical resonant frequency of the spring mass VLEG,the following two equations govern optimal coil characteristics and howit relates to the generator load resistance for maximal electrical poweroutput (Eq. 7a):

D _(e) =N ²(dφ/dx)² −R _(c) and R _(optl)=(N ² /D _(p))(dφ/dx)² −R _(c)when D _(e) =D _(p)

where D_(e) is the electromagnetic damping factor, D_(p) is theparasitic damping factor, N is the number of coil turns, dφ/dx is theflux gradient along the axial length of the cylindrical side of the PMAexiting or entering perpendicular to that surface and the direction ofvibration, R_(c) is the coil resistance, and R_(optl) is the optimalload resistance. By adjusting the wire gauge and the relative length inthe two sections of the variable wire gauge FCA coils, one can adjustthe spring mass VLEG to satisfy the above equations so that for a givenamount of vibrational wave kinetic energy falling upon the WEC repeatingcomponent of the EKS or any other device containing the present springmass VLEG structure, a maximal amount of kinetic energy is transferredto the rotor of the VLEG, the highest percentage of the incident waveenergy is dissipated, and the highest percentage of the dissipatedenergy is converted into electrical energy. Adjustment of either thespring constants, the resistance and the number of turns of the variablegauge coil series connected coil segments, and mass (2) (the mobilesubunit of the EKS in the embodiments described herein), and the loadresistance of the generator—once mass (3) of the PMA rotor and the sizeand strength of the magnets has been chosen, and the parasitic dampingfactor has been made as low as possible—can be performed to fine tunethe VLEG to an optimal kinetic energy dissipation function andelectrical power generation. The system of variable gauge coils, massspring system configuration, and compressive repulsion magnetic fieldtechnology PMA's in the given arrangement that possesses this manner ofoptimization for its desired function of vibrating wave energyconversion are distinguishing features of embodiments of the presentprinciples described herein.

The End Magnet Flux Focusing and Braking System

Referring once again to FIGS. 9A and 9B showing a side view of examplesof the first and preferred embodiment of the basic VLEG unit and thesecond embodiment of the basic VLEG unit, respectively, the end brakingmagnets 74 and 75 are noted again. It should be understood that in thediscussion below, the N pole designation may be changed to the S poledesignation without any change in any aspect of the functional operationand description of the end magnet flux focusing and braking system aswell as any other component of the present principles described herein.The end deflecting magnetic field magnets are not shown on the basicVLEG unit for purposes of brevity. The novel use of the end brakingmagnets in functioning to damp out excessively long motions of the rotorfrom particularly large waves as a component in the electromechanicalbraking system for the WEC repeating unit of the EKS has already beendescribed in detail. Here, in the basic VLEG unit, the upper N pole ofupper braking magnet 74 repels and decelerates PMA 37 to a stop everytime the end N pole of PMA 37 arrives in close proximity as a result ofa positive sloping half of a strong vibrational event. N pole on lowerbraking magnet 75 performs in the same manner when the lower N pole ofPMA 37 arrives in proximity to it as a result of the subsequent negativesloping half of a strong vibrational event. In the event of a wave trainof vibrational disturbances, the kinetic energy of the impinging wave isstored in the potential energy of the repulsive magnetic field betweenthe PMA N pole and the braking magnet N pole only to be released asuseful kinetic energy for power conversion on the subsequent movement ofthe rotor after the passage of the vibrational event. Thus, very littleof the incoming kinetic energy is dissipated as waste heat fromfrictional impact losses. Unlike the VLEG of the WEC, the basic VLEGunit does not incorporate shorted coil windings and braking springs aspart of the braking mechanism. Again note that the two braking magnetsthemselves are in repulsive field mode with respect to each othershowing yet another useful configuration of the unique use of repulsivemagnetic fields in the total configuration of all of the magnetic polesin the VLEG.

In addition to the braking function, the end magnetic magnets haveanother novel feature that drastically reduces flux leakage and wastageof magnetic flux lines from the PMA. FIG. 9C illustrates the magneticfield line configuration of the basic VLEG PMA, similar to FIG. 4B.While the flux leakage at the ends of the PMA magnetic structure unitthat do not impinge on the coil windings is much less than that as shownin the conventional attractive magnetic pole configuration as shown byFIG. 5B, nevertheless, the leakage is still considerable through theends of the PMA. However, FIG. 9D shows what happens to the magneticfield line distribution when braking magnets 74, 75 are used. The endmagnetic flux leakage drops drastically as N pole emerging flux lines45, 52 are “boxed” in and repelled, and the only destination that theyhave left to travel is to terminate on a nearby S pole, which in thisbasic VLEG unit, is the only repulsive magnetic field region of the PMA,the pair of S poles facing each other through the repulsive pole piece53. In large VLEG applications such as the WEC repeating component ofthe EKS of FIG. 3A, this magnetic focusing effect is much less marked asthere is considerable distance between the end of the PMA and thecorresponding braking magnet—the primary use of the braking magnet inthis category of applications is just braking. However, if one is usingsmall PMA VLEG units of one to three magnetic structures (two to sixmagnets, three to seven pole pieces) in length in such applications asmagnetic shock absorber energy generator, wind energy vibrationalgenerators, or surface small wave WEC's, and if the size of the magnetsare large, this magnetic focusing effect is truly an efficient way tostop magnetic flux leakage and greatly enhance the efficiency ofvibrational energy dissipation and electrical energy conversion.

When the stroke length of the VLEG, however, is much longer than thedistance between the ends of the PMA and the ends of the respectivebraking magnets that face them, to achieve the same focusing effect asdescribed above, we can add the end magnetic field deflecting magnets212 and 213 shown in FIGS. 9G and 9H. Exactly the same magnetic fluxline focusing effect is accomplished as in VLEG's operating over muchshorter stroke lengths. The functioning of this structural variant ofthe basic VLEG has already been described in detail.

Other design considerations of the electromagnetic spring brakingsystems include that the braking magnet magnetic pole should berelatively more powerful than the end rotor magnet pole of same polaritythat it faces; that the number of turns of wire shorted and the gauge ofthat wire can be varied as well as the stiffness of the braking springscan be varied to achieve a braking effect of variable magnitude; andthat the location of the shorted braking coils or copper shorting collarcan be varied to set the maximum size of the wave that the rotor will bepermitted to oscillate fully with.

The Vibrational Energy Electrokinetic Matrix Transducer

The Vibrational Energy Electrokinetic Transducer Matrix in exemplaryembodiments described herein is a three-dimensional array of VLEG unitscomposed in a lattice structure. However, it should be understood thatconfigurations or geometric structures other than a lattice structurecan be employed. In general, this wave energy conversion system caninclude a plurality of vibrational linear electric generators (VLEGs),where each of said VLEGs includes a field coil array and a permanentmagnetic array that is configured to induce an electrical current in thefield coil array in response to relative motion effected by wavestraversing a fluid medium in which the VLEGs are disposed, as discussedabove. FIG. 10A illustrates a side view cross section of an exemplaryarrangement of VLEG's structured as a 3 by 3 matrix or a total of 9 VLEGunits. This is more clearly seen in FIG. 10B which, in addition to thestructural components, shows a top view of the magnetic field linedistribution within the matrix. This arrangement of Linear ElectricGenerators is a distinguishing and advantageous feature, as it employsmultiple layers of LEG's, each containing the unique embodiment of theVLEG in such a way where the magnetic fields of one extends to and isfocused into all of its adjacent neighbors with a 3 dimensional matrixof PMA's interdigitating with a 3 dimensional matrix of FCA's. Withrespect to the range of distances separating adjacent VLEG's within aWEC, this range is dependent on, first, the amount of magnetic materialin each magnet used, which determines the dimensional size of themagnets, which in turn determines the size and intensity of thesurrounding magnetic fields, which then determines the thickness (thedifference between the outside diameter and inside diameter) of thecoils surrounding the magnets, and then this inter-VLEG distance isequal to twice that. For the prototypes constructed with N42 cylindricalmagnets possessing 200 pounds of magnetic pull with the dimensionspreviously stated, it was already explained that this distance wasmeasured and determined to be approximately 3 inches. For the smallestuseable N42 magnets with similar geometry with 20 pounds of magneticpull, it has already been explained that the distance was 1.4 inches.For the largest off the shelf cylindrical N42 magnets which possessmagnetic pulls of up to 1200 pounds and six times more magnetic materialper magnet, producing a scaling up factor equal to the cube root of 6equal to 1.44, the distance would be approximately 4.3 inches. Thus, therange of inter-VLEG distances in a multi-VLEG Electrokinetic MatrixTransducer would be approximately slightly above once inch to just underfive inches in preferred arrangements. When we add the effects of enddeflecting magnetic field magnets, end braking magnets, and highermagnetizations up to N52 as compared to these calculations involving N42magnets, we arrive at a practical range of about one inch to 12 inchesas the desirable and preferred range of distances. One can consider theuse of magnets of any size, thereby further enlarging the distanceseparating adjacent VLEG's, but the use of such large and immenselypowerful magnets in a WEC with many VLEG's would need specialengineering considerations with regards to assembly and the structuralstrength of the assembled structure.

Each of the individual 9 VLEG units in the embodiment one configurationof the PMA rotor 37 and the FCA 34 stator in this example function inthe same manner as previously described and there are no modificationsin the structural components other than now spring 23 functions as theupper perturbing force spring for all the units together, whereas lowerrestoring force spring 63 still are assigned to each VLEG unit. EachVLEG unit shown here is the basic unit of one PMA magnetic structuralunit plus one pole piece. 34-3 denotes coil windings of FCA 34 thatpoint down into the page, and 34-4 refers to those that point up out ofthe page. Structure 95, a VLEG and stator encasement shell composed oflower anchor plate 90, sides 95 and 95B and top plate 95C representsnon-magnetic casing out of suitable materials previously described thatcovers the whole LEG matrix to shield it from its environment whether itis from the ocean such as in the WEC of the EKS or in some otherenvironment. Perturbing force spring cable anchoring plate 95A isattached to force spring 23 at attachment point 73 allowing the latterto be attached to all 9 of multi-stand stainless steel cables 33 atupper cable attachment points 76C. Restorative spring upper attachmentpoints 79, lower attachment points 80, inner stainless steel tubes 36 incentral cavities 47, repulsive pole pieces 53, end pole pieces 51, 54,braking magnets 74, 75, cable 33 lower PMA attachment points 91, andupper PMA attachment points 74C are all as in the basic VLEG unitdescribed in detail previously. If it is desired to magnetically shieldthe VLEG matrix from adjacent structures, magnetic shielding 204 may beplaced around the matrix at a suitable distance so as not tosignificantly interact with the vertically oscillating PMA arrays.

Not shown in FIG. 10A is the structural enhancement to the PMAcomprising end magnetic field deflection magnets 212 and 213 of FIG. 9G,the structural and functional configuration of which has been describedpreviously in detail, that may be added to each of the PMA rotors ofFIG. 10A in the event, for example, that the rotor-stroke distance isappreciably greater than one half the axial length of the PMA structuralunit in each PMA such as in the given exemplary application comprisingthe WEC repeating unit of the present principles, the EKS. Thisstructural enhancement may be applied to all vibrational energyelectrokinetic matrix transducer structures described herein.

FIG. 10B indicates how the optional magnetic shielding 204 isconstructed; it is a three layered structure in this embodiment. Lookingat the inset bracketing magnetic shielding 204, 204A represents amaterial with a very high B saturation point (Magnetic Field FluxDensity), high permeability, low coercivity (resistance todemagnetization), and the ability to be applied in thin sheets; lowcarbon high silicon electrical steel (also known as transformer steel,μ_(m)=5000, B_(sat)=1.8T) is excellent for this as well as Giron™(μ_(m)=5000, B_(sat)=2.0T) or MagnetShield™ (μ_(m)=4000, B_(sat)=2.1T);204B represents a bonding layer of strong bonding magnetic epoxy such asJB Weld™; and outer layer 204C comprising very highly magneticallypermeable material such as Permalloy™, Ultra-Perm™, or Mu-Metal™(μ_(m)>400,000). The inner layer traps most of the leaking flux linesand whatever is left are made to travel only in the outer layer whereeventually, the flux lines will close their spatial loop onto a pole ofopposite polarity. It is fairly evident that while theoretically, thesecond embodiment of the VLEG, where the rotors are the FCA's and thestators are the PMA's, can be the component of a VLEG matrix, to havemany moving FCA structures and to collect electrical power from such acomplicated moving armature structure via slip rings or allowing looselyconstrained wires to be moved with the oscillations of the rotor wouldnot be a satisfactory arrangement from the maintenance and survivabilitystandpoint. Thus from a practical engineering standpoint, it is muchmore difficult to design the VLEG matrix transducer with a lattice ofmoving FCA rotors, though it can be done by those of ordinary skill inthe art based on the present description if an application requires it.The following description of the vibrational energy electrokineticmatrix transducer will be made with respect to embodiment number 1 ofthe VLEG.

An important feature of the Vibrational Energy Electrokinetic TransducerMatrix is the magnetic field flux distribution. Here, the plurality ofVLEGs are configured such that poles of given magnets of a givenpermanent magnetic array in a given VLEG in the VLEGs are adjacent topoles of opposite polarity of other magnets of another permanentmagnetic array of at least one other VLEG of the VLEGs that is adjacentto the given VLEG to concentrate a magnetic field through a field coilarray of at least one of the given VLEG or the other VLEG(s). Forexample, in the preferred embodiment illustrated in FIG. 10B, everymagnet pole of every PMA 37 of every VLEG is adjacent to an oppositemagnetic pole belonging to each of its adjacent neighbors. As a result,the flux lines emanating from the repulsive pole regions at the sides ofeach PMA are focused through the surrounding FCA 34 coils to createregions 88 of maximum flux densities within the coil regions to create amaximum Faraday induction effect through the entire matrix. Note that,as an added beneficial effect, in the spaces 89 between adjacent FCAstructures where there are no coil windings present, there is verylittle flux lines present, a most desirable feature. There is virtuallyno magnetic flux leakage and wastage through this advantageous effectwhich is somewhat less marked at the periphery of the matrix where theouter VLEG, especially at the corners of the matrix, are not next to themaximum number of four adjacent poles of opposite polarity such asindicated by Region 86. Nevertheless, flux coil linkage wastage isreduced even at the corners and the sides of the matrix. Thisadvantageous effect occurs because each internal PMA is adjacent toeight other PMA structures; four of them are closely adjacent and of theopposite magnetic polarity attracting flux lines from a N pole of thecentral PMA to a S pole of the four closely adjacent PMA structures; theother four PMA structures that are further away are in the repulsivemode like magnetic polarity configuration with the N pole of the centralPMA being repelled from the surrounding four less adjacent PMAstructures; each PMA along the side of the matrix is adjacent to 5 otherones, and each corner PMA is adjacent to 3 neighboring ones, and thusthe effect is less marked. The intense magnetic focusing occursthroughout the internal space of the matrix and one in effect has athree dimensional lattice of magnetic poles moving with relativevelocity to a 3 dimensional intertwined lattice of copper coilsresulting in Faraday production of electricity throughout every portionof the three dimensional structure. All of this magnetic fieldconfinement and focusing is done by the magnetic poles themselveswithout the need for heavy magnetic armature structures as found intypical electric generator arrangements. This drastically cuts down eddylosses, Lenz Law Back EMF drag forces, and hysteresis losses thatdecrease the efficiency of the of the electric power conversion.

Referring to FIG. 11, the structure of the 3-dimensional parallel VLEGElectrokinetic Matrix Transducer can be extended to structures of anysize in 3-dimensions all having the just described most optimaladvantages if, for example, a certain repeating structure that conformsto certain structural rules is followed. Referring to FIG. 11 whichillustrates a 2 by 5 by 3 VLEG Electrokinetic Matrix Transducer, we seethat each PMA column 97 comprises 2 PMA magnetic structure units 96 inthe y direction using a x, y, z coordinate system. The y directionorientation of PMA magnetic structural units into columns is given by105, the x direction orientation of PMA columns into a layer is given by106, and the z direction orientation of PMA layers into a 3-dimensionallattice structure is given by 107. Following previously defined rulesfor the PMA structure, where for each integer y greater or equal to 1,the number of VLEG structural PMA magnetic units in each PMA is y, thenumber of magnets in each PMA is 2y (even number), the number of polepieces is 2y+1 (odd number), the number of repulsive regions is 2y−1(odd number), the polarity of each end of the PMA are the same (two N ortwo S poles). There are 5 PMA columns present in the x direction formingone layer of PMA columns. The number and orientation of the PMAstructures 97 in a layer 99 are as follows: for integers x greater orequal to 0, the total number of PMA columns is 2x+1 (odd number), themagnetic poles of each PMA structure is in opposite polarity to themagnetic pole adjacent to it in each neighboring PMA structure on eitherside, and the end magnetic poles of the first and last PMA structurecolumns 97 are all of the same polarity (four N poles in total) but theend magnetic poles of adjacent PMA columns are of opposite polarities.Finally, the layers of PMA structures 99 are organized into a3-dimensional lattice in the z direction according to the rules that forintegers greater or equal to zero, the number of layers is equal to 2z+1(odd number), the magnetic poles of each layer are opposite in polarityto the magnetic poles adjacent to it in each layer in front of it andbehind it, and the end poles at the corners of the first layer and lastlayer are all of the same polarity (eight N poles in total). All of theend poles essentially should have the same (a common) polarity (S polesare equally acceptable and maybe interchanged with N pole designationsin this description) at the 8 vertices or corners of a rectangularcrystal-like lattice structure. Outlined in dotted drawing, additionalVLEG PMA magnetic structural units 98 can be added along with additionalPMA columns 104 that can be added and additional PMA layers 101 that canbe added to enlarge the matrix to any arbitrary size as illustrated inFIG. 11 consistent with stable mechanical stresses placed on thestructure and consistent with the relations set forth above. Theintertwined FCA matrix is represented by coil windings 103A (O's) goingout of the page and 103B (X's) going into the page. The order of theVLEG Electrokinetic Transducer is given by the product (2x+1) (y) (2z+1)where x and z are integers ≧0 and y is an integer ≧1. The number of PMAstructures which is equal to the number of VLEG's in the matrixtransducer is given by (2x+1) (2z+1).

For instance, the basic VLEG has x=0, y=1, and z=0. Hence its order is(2*0+1) (1) (2*0+1) or 1 and the basic VLEG Unit is a Vibrational EnergyElectrokinetic Transducer of order 1. The device of FIGS. 10A and 10Bhas x=1, y=1, z=1 and hence, the order of that VLEG ElectrokineticTransducer is (2*1+1) (1) (2*1+1)=9. Finally the device of FIG. 11 canbe given as x=2, y=2, and z=1 to give (2*2+1) (2) (2*1+1)=5*2*3=30. Theproduct (2x+1) (y) (2z+1) not only gives the order of the VLEGElectrokinetic Transducer, it also gives the total number of VLEG PMAmagnetic structure units in the matrix; the product (2x+1) (2z+1) givesboth the number of PMA structures, FCA structures, and Linear ElectricGenerators within the matrix. Any of these devices following this rigidgeometric structure can replace the VLEGs in the WEC's shown in FIG. 3A,FIG. 7A, and FIG. 7B, each of which has x=0, y=3, z=0 yielding an orderof 3. The only limit on the size of this structure that can be placedinto the WEC of the EKS is engineering considerations that accompany theuse of large and powerful magnets, the height of the waves whose energyis to be dissipated, weight considerations on the spring suspensionsystem, mechanical stress on the device caused by torsional andhorizontal components of wave motion on the WEC, and cost factors. Notethat the PMA lattice would be within the mobile subunit of the WEC ofthe EKS and that the FCA lattice would be within the fixed subunit ofthe WEC. Note that the multilayered magnetic shielding 204 of FIG. 10Bwould be located along the two face sides in the YZ plane and the twoface sides in the XY plane of the VLEG electrokinetic matrix transducerouter 6 sided surface of FIG. 11; shielding should not be applied to thetwo face sides in the XZ plane because of the direction of vibrationwhich is in the Y direction.

Further note that while FIG. 11 does not show end deflecting magneticfield magnets (212 and 213, FIG. 9G) on each component VLEG of the VLEGelectrokinetic matrix transducer, it may be added if so desired tofurther and greatly enhance the deflection of magnetic flux lines backinto the transducer instead of being lost to space as magnetic fluxleakage. As described previously, this option to do so would be employedif the end braking magnets of the VLEG, not shown in FIG. 11, arelocated significantly away from the ends of the PMA's if the strokedistance is significantly greater than the reach of the end magneticfields of the end pole pieces of the PMA's. Also note that if onecomponent VLEG of the VLEG electrokinetic matrix transducer is equippedwith a pair of end deflecting magnetic field magnets, they all should beto maximize effective functioning of the matrix.

To relate the order of the matrix transducer to the size of the incidentwave energy disturbance, we know that maximum kinetic energy of therotor develops when the PMA axial length is one third the rotor strokelength which should be equal to the significant wave height(s_(pma)=s_(r)./3=H_(te)/3) when the vibration is in the y direction ofFIG. 11. The number of PMA structural magnet units (SMU's) in each PMA,y, in the preferred most efficient configuration is equal to the PMAaxial length divided by twice the sum of thickness of one pole pieceplus one magnet (y=s_(pma)/2(T_(m)+T_(p)). Since in the preferredconfiguration, the number of coils for each PMA (SMU) is 4 whosecombined width is equal to that of the axial length of that unit, thenumber of coils in the stator will be 4 times the number of structuralmagnetic units times 3. That is, in the preferred embodiment, once themaximum significant wave height, thickness of the PMA pole pieces andmagnets are chosen for the given WEC design, the number of coils usedfor each PMA of each VLEG is 12 times the number of PMA SMU's used and 6times the number of magnets used. These relations hold true for any sizeVLEG electrokinetic matrix transducer from order one as illustrated inFIGS. 9A, B, G, H; order three as displayed in FIG. 3A; order 9 asdisplayed in FIGS. 10A, B; or order 30 as displayed in FIG. 11. Againnote that only the preferred embodiment number one of the VLEG (rotorPMA and stator FCA) should be used when there is more than one PMA (x>0,z>0). Also note that the coil number computed above represents the idealpreferred configuration for maximum electrical power output for a givensized wave determining a resulting sized PMA, but the number of coilsactually used may be less due to design considerations. However, thecoil number should not be less than 8 times the number of PMA SMU's or 4times the number of PMA magnets or else there will be a seriousdegradation in the efficiency of the device. These relationships holdfor when the VLEG Electrokinetic Matrix Transducer encounters oceanwaves of significant size that would ordinarily be present in the bodiesof water in which it is deployed.

There is one special case previously discussed with respect to oceanwaves, however, that allows the VLEG Electrokinetic Matrix Transducer tobe used in bodies of relatively calm waters with small waves that do notimpose a need to protect a structure or coast from damage of the kineticenergy of waves and hence, the transducer is being used strictly as anenergy harvesting device for conversion of this kinetic energy toelectrical energy. In this particular case, the stroke distance of thePMA rotor will usually be very small, usually quite smaller than the PMAlength itself. In this circumstance the ratio of the length of the FCAto the length of the PMA should, in order to prevent many of the coilsfrom never passing over a repulsive magnetic field area of space, beonly slightly greater than 1:1 rather than the 3:1 ratio that has beendescribed up to this point for use in ocean waves. More exactly, thelength of the FCA, in a preferred embodiment, should equal the length ofthe PMA plus twice the amplitude of the wave vibration or the waveheight. In this case, the number of coils in the FCA would be 4 timesthe number of SMU's in the PMA (or twice that of the number of magnetsin the PMA) plus X, where X equals the wave vibration height divided bythe thickness of each of the coils in the FCA. With this arrangement,virtually all coils will be almost always over a magnet, therebyproducing power and thus allowing VLEG's with long PMA's to be highlyefficient in producing electric power in calmer, smaller bodies of waterand its use generalized to other environmental circumstances such withwind, road and rail traffic, boat wakes, and surf vibrations, where theenergy vibrations maybe rather small. In fact two additionalcharacteristics emerge from this particular embodiment of the presentprinciples: 1) With small wave vibrations, the efficiency of wavekinetic energy to electrical energy conversion increases as the ratio ofthe PMA length (and hence the number of SMU's and coils) to the wavevibration height increases and 2) the previously defined lower usabilitylimit of magnets of at least 20 pounds of pull for the purpose ofemployment with commonly encountered ocean surface waves in preferredembodiments can be decreased to magnets that are significantly smallerboth in terms of magnet pull and dimensional scale. As an exemplaryquantity of magnet pull and size, the magnets can be as small as 0.25″o.d.×0.0625″ i.d.×0.25″ thick possessing a magnetic pull of 6.5 poundsleading to a coil thickness and inter-VLEG distance as low as (using tothe previously described process that applies the scaling method ofcalculation to the prototype laboratory measurements, this time with ascale factor here of the cube root of 32 or 3.17) 0.5″ and 1.0″respectively, thereby allowing for rather small embodiments of thepresent principles to be implemented for these low level vibrationalenergy sources.

This arrangement of uniquely structured VLEG's incorporated into a novel3 dimensional lattice of LEG's producing extraordinarily low amounts offlux leakage, Faraday Induction of electricity throughout a significantvolume of space created by a 3 dimensional matrix of PMA's oscillatingin relative velocity to a 3 dimensional lattice of FCA's, focusing ofmagnetic fields into coil arrays without the need for large heavyferromagnetic armature structures, thereby lowering hysteresis and eddylosses, and the unique structuring of the coils give rise to a totallynew and different manner of dissipating kinetic energy of ocean wavesinto useful electric power. The incorporation of this device into theWEC is an important and distinguishing aspect of the ElectrokineticSeawall repeating unit. In essence we may regard all of the PMA's in theVLEG transducer matrix as a 3 dimensional magnet PMA matrix rotor thatinterdigitates with and vibrates with respect to a 3 dimensional coilmatrix stator represented by all of the FCA's in the VLEG transducermatrix with the source of the vibration being applied to the VLEGtransducer matrix being the wave kinetic energy being incident upon theWEC repeating subcomponent that contains the transducer matrix. We haveessentially, a 3 dimensional linear generator, of which the basic WECand VLEG units of FIGS. 3A, 7A, 7B, 9A, 9B, 9G, and 9H are the simplestconfigurations. There is one VLEG electrokinetic matrix transducer ineach WEC repeating subcomponent making up the EKS that comprises thepresent principles.

Tethering, and Electrical Power Takeoff

In one embodiment of this portion of the present principle, side viewFIG. 12A illustrates an Electrokinetic Sea Wall that is tethered by acable 111 connected between the top plate 5 of and shown for one fixedsubunit just below the base of the mobile subunit 2 and a fixedanchoring structure 110 on the seabed floor 108 where electric cable109A takes generated electrical power away. A power take off cable 109hangs downward as part of cable 111. 112 represents the ocean surface.114 indicates a tether connecting the last WEC repeating component 114Ato a tethering point on the shoreline or to additional WEC's. 6represents a tether connecting adjacent WEC repeating components. Aspreviously discussed, 1, 2 and 22 represent the buoy mobile subunit top,base, and the inertial liquid wave dampening system (ILWDS) respectivelywhile 113 represents the rotor slide tube structure. In the secondembodiment of this portion of the present principles, side view FIG. 12Billustrates the EKS as rigidly attached to the seabed floor by means ofa hard fixed pole or pipe 115 attached to the top plate 5 of and shownfor one fixed subunit. The power take off cable may either reach theseabed floor by traveling within the anchoring pipe, or freely hangingdown to the seabed floor in a separate manner. FIG. 12C depicts a topview of a third embodiment of this portion of the present principleswhere the tethering mechanism is a rigid one by which each WEC 114A isrigidly attached via its fixed subunit (not shown) to the adjacent seawall, pier, or bulkhead 118 by rigid metal braces or connectors 117.Because the WEC's are attached by rigid means, for smoothly straight orcurved seawalls, exemplary distances between the adjacent WEC's mayrange from only approximately 10 centimeters for smaller sized WEC's toa distance equal to that of the largest cross-sectional diameter of thebuoy floatation collar base 2 of the largest WEC's which can be up to 10meters in diameter with this distance being smaller for concavely curvedsea walls and larger for convexly curved sea walls. Also, if the seawallis an indented bulk head such as 118 and it is intended to have the EKSclose in proximity to the bulkhead for reasons of structural stabilityof the brace and for absorbing as much kinetic wave energy from both theoncoming waves and waves reflected off the bulkhead, the inter-WECdistance should be in the preferred configuration approximately somewhatmore than the width of a convex section 118B of bulkhead as shown, adistance in the range of about 0.5 to 2 meters. The preferredarrangement for the rigid tethered distance between a smooth seawall andthe EKS should be at least the greatest diameter of the cross-sectionalarea of the WEC, which can range from approximately 10 centimeters to 10meters and, for bulkhead seawalls of the form and structure 118, notlarger than a concave section 118A if it is desired to bring the EKS asclose as possible to that bulkhead. The power take off cable 119 runsfrom each WEC repeating unit of the EKS to form an above ground powercable 119A on the conventional seawall, which in this illustration is ametal bulkhead 118 behind which is the land 120. Floatation buoy collartop 1 and base 2 and rotor oscillation structure 113 are also displayed.

If the embodiment of the EKS is not rigidly attached to the seawall butrather is freely floating in the vicinity of the seawall, the inter-WECflexible tethering distance should be as previously described to preventcollisions from wave tipping of the WEC's and the EKS should be tetheredin a floating manner by non-rigid cables to a seabed anchoring mechanismsuch as 110 in FIG. 12A, and FIG. 13C, as well as anchor 193 in FIG. 12Dand FIG. 12E (1); at least two cables in number for positional stabilityrelative to the seawall should be used, but, if necessary, additionalcables would be employed so that the closest possible approach of theEKS to the seawall even when exposed to large waves and strong driftingcurrents should be no closer than 4 mobile subunit buoy floatationdiameters of the range just described.

The fourth embodiment is illustrated in side view FIG. 12 D, which showsa heavy metal brace 194 that in effect converts all of the ILWDSstructures 22 of the fixed subunits of the repeating WEC components 114Ainto one rigid stabilizing structure to which cable 111 is attached toanchor 193, which is attached to seabed floor 108. Again power cable 116is attached to the seabed floor 108. For the purpose of having the EKSbeing tethered, it is important to note that the massive mass reactioneffect of this brace 194 makes it unnecessary for the EKS to be anchoredat all if so desired and cable 111 and anchor 193 can be done away with.If it is desired to have the EKS be freely floating, tether 114 anchoredto the shore line or to a conventional seawall can be omitted.Furthermore, since each WEC is anchored rigidly via its fixed subunit tothe brace lying beneath it, tethering springs 6 could be omitted ifdesired for greater simplicity of the structure. The heavy metal braceitself can be rigidly tethered to a nearby seawall. The heavy metalbrace converts the embodiment to a rigid EKS so that all tetheringdistance considerations described above for the rigid tethering to aseawall would apply. Sufficient buoyancy material of the samecomposition as previously described for both the mobile subunit 19 andthe fixed subunit 20 is added in the form of blocks or rings 30 on eachILWDS 22 and 30A on brace 194 so as to make the entire structurecontaining the EKS and its repeating components subunits neutrally orslightly positively buoyant. The center of mass and gravity of theentire structure is deep in the water well below the surface and belowthe structure's center of buoyancy to create stability of the combinedfixed unit composed of all the WEC fixed subunit structures with respectto the surface wave oscillations. The fifth embodiment of this portionof the present principles is shown in side view FIG. 12 E (1) as aradical enhancement of the previous embodiment in which the brace 194has been replaced by a massive boat-like structure 195 rigidly attachedto all of the fixed subunits of the WEC repeating components of the EKS.Aside from making the fixed anchorage via cable 111 and anchor 103 inFIG. 12E (1) optional allowing the EKS apparatus to float like a boat,it has enormous implications to the stability and efficiency with regardto dissipating ocean wave kinetic energy to be explained in themechanism by which embodiments of the present principles achievestabilization in the ocean, as discussed herein below.

Ocean Wave Stabilization of the EKS

To this point, keeping the reaction mass (1) formed by the fixed subunit20 of the WEC containing the stator FCA 34 of the VLEG relativelyimmobile with respect to the mobile subunit 19 reaction mass (2)containing the rotor PMA 37 reaction mass (3) of the VLEG has beenexplained to be important in order to develop significant relativevelocity of the rotor relative to the stator from the ocean wave frontimpinging on the EKS. Most of the reaction mass (1) and thisstabilization function was produced from the large inertial mass ofmetal and entrapped water in the ILWDS 22 of the fixed subunit 20 of theWEC. This method of stabilization and immobilization of the individualfixed subunit 20 of the present principles so far described wereprimarily represented in the ILWDS and are advantageous over othermethods for this kind of wave stabilization, such as heave platestructures. Now to be described is a radical improvement in thisstabilization function that is unique to the present principles and isshown in FIG. 12 E(1) (side view) and FIG. 12 E (2) (top view). Inparticular, a plurality of WECs can be enveloped by and tethered to asemi-enclosed container that is configured to be at least partiallysubmerged within the ocean and to be filled with ocean water. Here, thecontainer, when disposed in the ocean, has a center of mass at a depthbelow the surface of the ocean that is sufficient to render thecontainer relatively stationary when the waves traverse over thecontainer. For example, instead of just a heavy metal plate braceconnecting all of the fixed subunits via their ILWDS together, we have astructure with the same buoyancy characteristics of an iceberg or largeoil tanker that is submerged to the major extent in the ocean. This“boat mass” of metal, which may be water filled like the weight chamber10 of ILWDS 22, represents a truly massive reaction mass (1) relative toreaction mass (2) represented by the mobile subunit and is equal to thecombined masses of all the fixed subunits in the EKS plus the mass ofthe metal and water entrapped in the “boat mass” 195. This huge mass,which is on the order of 10 to 100 tons and from an engineeringstandpoint can be made as large as a supertanker of 3 orders ofmagnitude larger, is held neutrally to slightly positively buoyant withthe center of buoyancy just beneath the surface of the water and thecenter of gravity and mass very deep in the water relative to the centerof buoyancy as a result of buoyancy blocks 198 made out of the samematerial as the buoy floating collar mobile subunit 19 and the buoyancyblocks or collars previously described for the fixed subunit 20. It isimportant that the center of gravity should be as deep below the surfaceas possible because horizontal force and velocity vectors and the moresignificant vertical force and velocity vectors of the wave motion,which would tend to oscillate the boat mass, decrease with the square ofthe depth beneath the ocean's surface. The precise location of thecenter of buoyancy is adjusted by suitable amounts of buoyancy materialattached to the heavy reaction mass (1). The buoyancy material andweight of the “boat mass” 195 would have to be distributed in such amanner to prevent unstable rolling motions in the directionsperpendicular and parallel to the long axis of the structure, by whichthe stability of a boat oscillating in the waves would be accomplished.The “boat mass” 195 comprises the buoyancy blocks or rings 198 attachedto each of 4 “boat mass” columns 197 and a massive metal plate 195Awhich may be water filled. This massive metal plate can be square,rectangular, circular, or any geometric shape. The buoyancy blocks mayprotrude slightly above the ocean surface 112 especially during wavetroughs. The individual WEC repeating components are tethered togetherby springs 6 in the previously described manner. Because each of theWEC's are rigidly attached to the boat mass, tethering springs 6 couldbe omitted for greater simplicity of this structure. If “boat mass”plate 195A is water filled, air can be pumped in and out through ingressand egress holes as previously described for the ILWDS of the WECrepeating unit and the one way air valve and air hose system shown ifFIG. 3A; this water ingress and egress system is not shown on FIG.12E(1) for ease of illustration.

To illustrate the function of this embodiment of the EKS apparatus,which is now more of the form of a floating platform, it may bedescribed as functioning like a large iceberg which has 87% of its massbeneath the ocean's surface. Its massive inertial makes it immobilerelative to the ocean waves that impinge upon it. Now if we create asmall lake in the middle of the iceberg and allow it to connect with theocean, and place a WEC in that small lake with the fixed subunit firmlyanchored at the bottom of the lake to the iceberg, and we now allowwaves to impinge upon the iceberg and go into the lake in the middle ofit, the mobile subunit would rise and fall with the passage of wavecrests and troughs while the fixed subunit would be totally andcompletely fixed to the massive iceberg resulting in the rotor of themobile subunit being accelerated up and back in the vertical directionrelative to the stator in the fixed subunit which is fixed solidly tothe massively immobile iceberg, thereby producing the necessary relativemotion between the rotor and stator that is required for the operationof the present principles.

The massive “boat mass” functions as does the iceberg. The fixedsubunits of the array of WEC's attached to the “boat mass” 195 by way ofthe ILWDS 22 seen on each WEC (shown as 191 in FIGS. 1A and 11C in FIGS.2A, B, and C) are totally and solidly fixed in position for all but themost gigantic waves. At the same time, the ocean waves may travelthrough the array of WEC's forming the EKS coming from any directionwith no deterioration of efficiency as a function of the direction ofwave propagation (shown as 196 in FIG. 12E (2)) where it is illustratedthat unattenuated waves 16 coming from any direction pass through thefour “boat mass” columns and become attenuated waves 17 with respect totheir kinetic energy. This action is omnidirectional—the direction ofpropagation does not make any difference in the efficiency of the EKS toattenuate wave energy. No steering mechanism is required in contrast tomany other types of wave energy converters. Thus, a large area of oceancan be covered by these EKS arrays attached to boat masses and wavekinetic energy can be attenuated over large tracts of ocean area, whichin and of itself is believed to be a novel aspect of the presentprinciples.

Electrokinetic Sea Wall Mesh Arrays

While exemplary embodiments of the present principles were described aswave kinetic energy dissipating devices in the form of a sea wall typeof barrier, the technology comprising the EKS can take another form.Already discussed is the ability of many small VLEG's in WEC's withsmall rotor strokes to replace one large VLEG in a WEC with a largerotor stroke. It is possible to have all of the WEC repeating componentsof the EKS to occupy a lattice configuration of any of many geometricshapes that can cover a significant space of ocean. Large waves enteringthis region of ocean from any direction of propagation can be completelyattenuated over the length of the wave front impinging the EKSapparatus. In this configuration, the EKS apparatus is given thenomenclature of Electrokinetic Sea Wall Mesh Array. Referring to FIG.13A, we see a top view of a geometrically square mesh array of 5 WEC'srepeating units 11C on a side for a total number of 25 WEC repeatingunits with each WEC tethered by springs, chains, or stiff cables 6 withthe spring being the preferred embodiment to its 4 nearest membersexcept along the periphery of the mesh where the tethering is to eithertwo or three nearby neighboring WEC's. The materials used for tether 6should be non-corrodible in sea water and quite strong and may includestainless steel chains and multi-stranded cable, nylon and polystyrenerope, Kevlar™ cable and/or other suitable materials well-adapted to themarine environment. Because the tethers should withstand the forces ofthe largest storm waves which will be sufficient to possibly move eventhe individual WEC fixed subunits and their ILWDS's, the tensilestrength of these tethers should be at least 500 pounds for the smallerWEC units and at least several thousand pounds for the larger WEC units,and the tethers should be sufficiently rigid yet flexible to allow somerelative motion of one WEC with respect to its neighboring WEC's but notsufficient motion to cause them to crash into each other with resultingdamage from the propagation of very large waves through the EKS MeshArray. The preferred arrangement is to use stainless steel springs withlarge spring constants on the order of 10 to 100 pounds/inch and of alength sufficient to keep the spacing between adjacent WEC's at leastequal to 4L(sin θ), where θ is the tipping angle from the vertical andis at least 60° in preferred embodiments. As the size and mass of theWEC increases, the spring constant and spring length should increase ina proportional manner. The preferred arrangement for the EKS Mesh Arrayis to use springs of lower spring constants and shorter lengths forsmall WEC's that would allow for this embodiment of the presentprinciples to take on the structure of a floating ocean energy absorbingcarpet that absorbs kinetic energy and converts it into electricalenergy over the entire surface of the mesh providing a structure withexcellent storm survival capabilities.

The issue of magnetic interaction between adjacent WEC's with internalvery strong and large magnets comprised within should be taken intoconsideration. For densely packed EKS meshes with closely spaced WECrepeating subcomponents, aside from the need for spacing to preventcollision events, one also has to allow for possible magneticinteraction via repulsion or attractive forces between adjacent WECsubcomponents. If the magnets used are sufficiently large and powerful,flexibly but not rigidly tethered WEC's might be adversely repelled orattracted by their neighbors with the possibility of serious damage tothe EKS mesh. Thus, the inter-WEC distance should be the larger of thetwo distances, S_(c), the minimum collision safety distance, or S_(M),the minimum magnetic interaction safety distance, the latter being givenby a known rule that strong magnets should be separated fromelectronics, other magnets, and ferromagnetic objects by a minimum safeseparation distance, s_(M), which equals 4 inches plus one additionalinch for every 10 pounds of pull exhibited by the magnet in question.Thus, a WEC that houses a PMA using magnets with a pull force of 1200lbs, the largest off-the-self commercially available industrial magnets,would produce an uncommon situation where such WEC repeatingsubcomponents tethered by flexible means should be no closer than 10.4ft even if the collision safety distance, s_(C), of two adjacent WEC'swith a buoy floatation collar height of 2 ft above the ocean surfacewould be 4L sin(60°) would be 6.9 ft. The magnetic interaction is ofsignificantly less concern if the WEC's are of a lesser size (lesserlength or weaker magnets) or are tethered by rigid means. A magneticshielding, such as that described in FIG. 10B, can be employed todecrease the inter-WEC distance to that of the minimum collision safetydistance, a desirable configuration as adjacent WEC's should be as closeas possible for improved wave energy attenuation.

FIG. 13B shows in more detail a side view of a single WEC in schematicform 11C (side view) of the basic structure described repeatedlypreviously. Again present in FIG. 13B are the FCA stator 34, PMA rotor37, ILWDS 22, upper perturbing force spring 23 and lower restorativeforce spring 63, mobile subunit 19, and fixed subunit 20. FIG. 13C givesa side oblique top view showing springs 6, WEC's 11C, four tetheringcables 111 tethering the EKS mesh array to sea bed floor anchoringpoints 110, and power collection cable 112 exiting from the mesh arrayPower Collection Circuitry of the mesh (not shown). Note also, the “boatmass” EKS inertial reaction mass stabilizer structure 195 attached toeach Inertial Liquid Wave Dampening System (ILWDS) 22 with four columns197 (three shown) extending above the ocean's surface is also presentand illustrated in dotted lines to indicate that it may optionally beused with the WEC mesh array to create a rigid massive structure and mayoptionally replace the four tethering cables and anchoring points if itis desired to have the EKS mesh array freely floating. The preferredembodiment is to use both structures, the “boat mass” structure 195 andanchoring cables/points 111/110 to provide stabilization to the mesharray as a whole both in terms of vertical oscillation of the fixedsubunits 20 and location of the mesh array in the ocean respectively.When both structures are used, the waves can approach the EKS mesh arrayfrom any direction, no steering mechanism for the EKS mesh array isneeded, the EKS mesh array is prevented from drifting aimlessly in thecurrent, and finally, all of the fixed subunits 20 are braced togetherby the “boat mass” 195 to form one extremely stationary reaction mass(1) against which all of the mobile subunits 19 (reaction masses (2))can develop efficiently a rotor velocity relative to the stator in thefixed subunit. Each row of WEC's 11C dissipates a fraction of the wavekinetic energy, and if the efficiency of each row of WEC's indissipating the energy of the wave is defined for each row asE_(ff-row)=(E_(wave-in)−E_(wave-out))/E_(wave-in) (it is assumed to beconstant for each row), where E_(wave-in) is the energy of the wave asit enters the row and E_(wave-out) is the energy of the wave as itleaves the row, and if there are n number of rows, E_(ff-mesh) equalsthe sum for all rows of this equation for each row. It can be shown thatfor an n row mesh array, the E_(wave-out) after n rows equalsE_(wave-out-of-mesh)=(E_(ff-row))^(n)×E_(wave-into-mesh) and theE_(ff-mesh)=(E_(wave-into-mesh)−E_(wave-out-of-mesh))/E_(wave-into-mesh),where E_(wave-out-of-mesh) is the energy of the wave as it leaves themesh array, E_(wave-into-mesh) is the energy of the wave as it entersthe mesh array, and E_(ff-mesh) is the efficiency of the mesh array. Onecan have sufficient number of rows so that the wave kinetic energyabsorbed by the mesh array approaches zero percent of the incident waveenergy. However, after a certain number of rows the amount of energyabsorbed by each succeeding row of WEC's becomes more and morenegligible. The sum of the rotor stroke distances of the WEC repeatingunit forming each row should approximately equal the significant heightof the largest practical waves that of which it is desired to dissipateits energy. Alternatively, the EKS mesh array can be replaced by alinear single row EKS array although the rotor stroke distance would bemuch larger, and the WEC's would be more difficult to engineer, moredifficult to design for storm conditions, and involve more costly WECrepeating units whose rotor stroke distance is equal to the height ofthe wave and equivalent to the product of the stroke distance of thesmaller mesh WEC and the number of rows in the mesh. Furthermore, thedensity of the EKS mesh array can be much higher, as the minimuminter-WEC distance given by S=4L sin 60° incorporates a very liberalsafety factor (or even less as previously explained), where L equals theheight of the fixed subunit and L goes up considerably for the largerWEC repeating units. One should note that theoretically any VLEGElectrokinetic Matrix Transducer of any order can be placed in the EKSmesh array WEC repeating components, but since these WEC's are designedto be small, matrices of order 1, 2, or 3 (a single PMA with 1, 2, or 3PMA magnetic structure units (y=1, 2, or 3)) are more practical.Survivability of the EKS mesh array in large sea storm waves would beexpected to be better than that of large WEC structures that have to bespaced far apart for such eventualities; the mesh would float like acarpet on the ocean's surface. For ocean or other water bodies likechannels or inlets where wave propagation is more or less always in thesame direction, square or rectangular EKS mesh arrays would be thepreferred arrangement with the longer dimension of the arrayperpendicular to the propagating wave front; for open water locationswhere the wave propagation is omni-directional, then circular or higherorder polygonal structures would be more desirable. Note that knownarrangements of other types of vertically oscillating WEC's have usedarrangements of multiple units that were quite farther apart than thepresent principles, greatly reducing the efficiency of energy capturingfrom the propagating waves. It is believed that the maximum spacing ofthe WEC repeating subcomponents should be such that the spatial distanceof each WEC from any of its nearest neighbors in any direction away fromthat WEC should not be any greater than approximately 8 times the heightof each floating buoy collar of each WEC above the surface of the ocean.The basis for this maximum spacing are the following two conditions: 1)The maximal magnetic interaction extending out from today's mostpowerful rare earth commercial magnets will not extend out to thisdistance and 2) Any wider spacing seriously degrades the kinetic energyextraction ratio (kinetic wave energy flowing into the EKS minus thekinetic wave energy flowing out of the EKS—that quantity which is thendivided by the kinetic wave energy flowing into the EKS) of the EKSarray; the spacing between adjacent WEC's in a row perpendicular to thedirection of wave propagation will degrade this wave kinetic energyextraction, and the larger the spacing, the greater the degradation.This degradation if not controlled leads to two problems—1) the amountof kinetic wave energy extracted over the area of the ocean in which theEKS is deployed becomes too limited to incur sufficient protection ofstructures behind it and 2) the magnitude of the by-product of this wavekinetic energy dissipation function, the production of useful electricalenergy, is seriously degraded as well. This spacing problem can beovercome by increasing the number of rows of the EKS from a linear arrayof one row to the 2 dimensional geometrically variable array of manyrows of the mesh arrangement. However, this multiple row meshconfiguration will most effectively make up for the spacing issue if thespacing between each WEC described above is less than the specified 8times the height of each WEC above the water; spacings greater than thatspacing lead to a degree of degrading of the energy extraction ratiothat the institution of a 2 dimensional multiple row configurationcannot likely overcome. Other arrangements of vertically oriented WECnetworks fail to take into consideration the spacing problem and in suchconfigurations, the individual WEC's that contain linear electricgenerators are spaced far too wide both for any meaningful wave kineticenergy attenuation for coastal structure protection, and fail to extractin a useful way as much electrical energy as can be extracted from thegiven area of the ocean in which these networks are located. The spacingdegradation problem is greatly attenuated by rigidly tethering the fixedsubunits of the individual WEC's to the seabed, an adjacent fixedconventional sea wall or other fixed structure, a large metal braceplate, or the large “boat mass” as described previously; a very massiveILWDS and fixed subunit would accomplish the same purpose; by such meanspreviously depicted in FIG. 12B through 12E, the movement of the mobilesubunit away from the vertical can be reduced by such an extent thattethering distances at least for the smaller WEC repeating subcomponentsof the EKS could be reduced to as little as several inches.

A circular EKS mesh array structure is depicted in FIG. 13D and FIG.13F, which provide top view illustrations of the arrays. In FIG. 13F,the density of the springs 6 is approximately twice that of thestructure of FIG. 13D, which makes for a more strengthened array thoughat the cost of flexibility. WEC's 11C (top view) in the FIG. 13F have agreater number of tethering springs between adjacent neighbors. Therewill be applications where the rigidity strength parameter is traded offfor flexibility. FIG. 13E shows the EKS array in side view. Againanchoring cable 111 and power collecting cable 112, anchoring plate 110,springs 6 and WEC structures 11C (side view) are shown. Likewise, as perFIG. 13C, the fixed subunits of all of the WEC structures 11C may berigidly tethered together with a “boat mass” structure. Also illustratedis an interesting application where a structure 146, which may be abuoy, a seafloor attached tower or some other structure, in the centerof the EKS circular mesh array receiving the benefit of wave protectionfrom the mesh array surrounding it. Here, a plurality of WECs areconfigured to envelop a structure 146 to dissipate the mechanical energyof waves that traverse into the structure.

Electrical Power Collection Circuitry

Once the kinetic wave energy has been has been dissipated by embodimentsof the present principles and converted into electrical power, theelectrical energy needs to be collected through an electrical PowerCollection Circuit or Circuitry (PCC). FIG. 14 depicts a block diagramof an exemplary embodiment of an Electrokinetic Seawall apparatus whichindicates the function of the PCC. Ocean waves propagate into WEC 1,2 .. . and n, with WEC 1 broken up into a block diagram of the MobileSubunit and its component Buoy Floatation Collar Unit and SpringSuspension System and Mechanical Wave Impedance Matching Section ofwhich the rotor is part; the Fixed Subunit composed of the Structuraland Buoyancy support, the Inertial Liquid Wave Dampening System (ILWDS),coil voltage rectifier and filter electronics, and the stator; and therotor of the Mobile Subunit with the stator of the Fixed Subunit formingthe VLEG. The Power Collection Circuit consists of the coil voltageoutput rectifier and filter electronics that is part of each VLEG, aMultiple Input DC Power Aggregator Circuit which combines the many DCoutput voltages and currents from the FCA rectifier and filter circuits,and sends the DC power out unchanged, for storage in a storage battery,converted to a DC power source of a different voltage via a DC to DCconverter, or converted back to AC of a voltage suitable for aparticular application. Note that a small amount of DC power is takenfrom the direct DC out line for the LED modules (205 FIG. 1A) used toilluminate each WEC making the EKS visible to passing ships. Finally,because large units are capable of producing large amounts of electricalpower in remote tracts of ocean, a method of internet-based videomonitoring and control signals are used. Not shown is the possible useof computerized monitoring and control circuitry that may be used tobetter regulate the behavior and output of the electronics used in theapparatus. In accordance with one advantageous aspect of the presentprinciples, very many DC voltage outputs that have a range of low tointermediate levels of output power are combined through the use ofmulti-phase rectifier filter and power aggregator circuits for thepurpose of vibrational electrical energy harvesting over a significantarea of energy producing surface. The configurations of the multi-phasefull wave rectifier filter circuitry and associated Multiple DC PowerSource Aggregator circuits used in embodiments of the present principlesinclude several advantageous features, as discussed in further detailherein below. The PCC may take several preferred embodiments dependingupon the configuration of the WEC repeating units of the EKS. Not shownis possible automated computerized monitoring circuitry that monitorsand influences the electrical power output; this circuitry should beemployed for survivability, efficiency, and safety reasons in largeinstallations of the EKS.

The block diagram of FIG. 14 also shows several important safetyswitches in the electronics and the Power Collection Circuitry of apreferred embodiment of the present principles. First, when a WECrepeating unit of the EKS apparatus needs to be serviced or replaced,means should exist to shut down the PCC for that WEC to avoid electricshock hazard; switches 210 function in this manner and disconnects thePCC of that WEC from the PCC of the entire EKS apparatus. Second, whenthe WEC is to be replaced or serviced, means should be provided so thatthe PMA, whose mass might be considerable in larger units, does notoscillate violently as the WEC is manipulated, which not only representsa mechanical danger from large powerful magnets moving unpredictably butalso represents a potential electric shock hazard from the voltagegenerated by the PMA moving unpredictably relative to the stator. Themeans by which these problems are ameliorated is accomplished in thisembodiment by FCA shorting switch 209A which shorts out all of the coilsof the WEC. This by itself will cause the electrical output of the VLEGin the WEC to fall to zero. In addition, shorting out the FCA coils willresult in a relatively high current flow in the shorted coil windingsproducing significant Lenz's Law back EMF forces on the PMA which willgreatly retard the extent and forcefulness of any of its movementsduring maintenance manipulation of the WEC, greatly reducing any chanceof mechanical instability and subsequent injury to personnel. Thisconsequential result is of further benefit in that it also will cut theelectrical power generated by the FCA coil windings to practically zero,virtually eliminating any chance of electric shock hazard to personnel.Water sensor switch 64A that sits at the bottom portion of the rotorslide tube is attached to the fixed subunit stator in an appropriateposition as low as possible suitable to the detection of water in thebottom of the rotor chamber of the WEC, a condition that can lead tocatastrophic electrical failure. The switch 64A is in series with switch210 and is designed to shut power off from the WEC if it detects seawater or other water in the bottom of the rotor slide tube. One otheradvantageous aspect of the mechanical and electric safety mechanisms ofthe present principles is switch 211; this switch, which shuts off thepower output of the PCC for the entire EKS apparatus, is remotelycontrolled and may be controlled from great distances via the internetas the preferred method of remote control and may be part of anycomputerized monitoring and control circuitry that can be added to theapparatus; when it is desired to shut down the entire EKS apparatus,this switch is opened, disconnecting all of the PCC from the outputpower takeoff cable that removes electrical power from the EKS. Such acircumstance would happen, for example, if weather forecasts predict aviolent storm that would be expected to arrive at the location occupiedby the EKS apparatus, which possibly may be in a remote and hard toaccess location, and it is desired to shut down the EKS in advance ofthe storm or for any maintenance procedure. This feature greatly adds tothe survivability of the apparatus in severely adverse weatherconditions which already is significant given the paucity of movingmechanical parts composing the EKS.

The video monitoring system of the present principles, which isconsistent with the current art of video monitoring technology, employsa system technology developed by Livevideomonitor.com™ that comprisesextremely simple internet-connected high resolution video cameras andremote control on and off switches that can respond to certain hazardousconditions such as water within the VLEG rotor sliding tube that may beoperated via a satellite internet communications link. The purposes ofthis system include: 1) monitoring visibility, weather conditions andwave heights especially for dangerous weather conditions; 2) monitoringthe proper functioning of the lighting system of the EKS so thatshipping will be aware of its presence; 3) turning either parts or allof the system off in the event of operational failure, the advance ofdangerous storms into the area of the EKS, and for maintenance andtesting done via switches 209A, 210, and 211 which may be connected forremote control operation; 4) detecting via water sensor switch 64A theleakage and presence of sea water, which can be corrosive, leading tocatastrophic failure of the WEC in terms of consequences both to themagnets and the coils, within the internal rotor slide tube 32 space ofthe VLEG; 5) collisions and other structural damage that suddenlydevelops. Because this system should remain operative after mechanicaland electrical failure possibly having developed, it would obtain itselectrical power from the storage battery rather than directly from thepower collection circuitry (PCC).

In accordance with exemplary aspects, the power collection circuit caninclude a plurality of field coils in which electrical currents areinduced. Here, each field coil provides a current at a different,respective phase. As discussed in the examples of POCs herein below, atleast one bridge rectifier circuit can comprise sets of Schottky diodesthat are each coupled to a respective field coil of the plurality offield coils to rectify the current from the respective field coil toenable harvesting of electrical power produced from the induction in thecoils.

For example, FIG. 15A shows a schematic of the PMA rotor 37 and FCAstator 34 of the basic unit VLEG comprising PMA 37 with one magneticstructural unit, four copper coils, 34-1 through 34-4 with lead pairsAB, CD, EF, GH respectively collectively designated as 121A-H; the coilshere are shown in the preferred but not exclusive arrangement of eachcoil being approximately equal to or just slightly larger thanone-quarter of the length of the PMA, that is, their combined width isapproximately equal to or just slightly larger than the length of thePMA. As shown in FIG. 15 B, relative motion of the rotor 37 with respectto the stator 34 due to wave oscillation will give rise to voltagewaveforms in coil circuits A-B, C-D, E-F, G-H that are 90° sequentiallyout of phase with each other giving rise to a 4-phase AC circuit thatwill be rectified to produce 90° out of phase unfiltered DC voltage waveforms that are subsequently smoothed out by at least one of theexemplary filtering circuits illustrated in FIGS. 15C, 15D, 15E, and15F. All four of these rectifying and filtering circuits can be used inthe PCC and will now be described. The diodes used in all four of theseexemplary circuits are Schottky barrier power diodes, type 40 PIV 3ARK44; other such diodes with higher PIV and current ratings may be usedfor larger configurations of the WEC.

FIG. 15C depicts circuit 127 which includes a 4-phase bridge full waverectifier circuit with filtering capacitors. Coils 34-1 through 34-4 areconnected via lines AB, CD, EF, and GH as shown to 4-phase full waveSchottky rectifier diodes D1-D8. Schottky diodes are advantageously usedin a 4-phase bridge rectifier (and may be used in full wave rectifiersof any higher phase) because, in small lower power VLEG units,minimizing ohmic power losses in diode junction regions are important tothe efficiency of such a device. Preferred embodiments of the PCC employSchottky diodes despite their slightly increased cost for severalreasons. For example, ohmic resistive losses, which can dissipate asignificant amount of the power produced in a low voltage LEG, increaseas the junction forward voltage drop increases. The pn junction voltagedrop across standard silicon power diodes is 0.5 to 0.6 volts. Further,germanium diodes have a junction voltage drop of about 0.3 volts and arevirtually impossible to obtain on an economical basis for currents ofgreater than 0.2 amperes. However, the voltage drop across Schottkydiode junctions is as low as only 0.1 volts, thereby ensuring that ohmicresistive losses are minimized and the efficiency of the VLEG units isoptimized. The use of Schottky diodes in 4 phase and higher full wavebridge rectifier configurations is believed to be a novel feature.

As illustrated in FIG. 15C, the output of the bridge rectifier formed bydiodes D1-D8 is filtered via filter capacitor C1 with a value that islarge on the order of 10,000 microfarads but the exact value isnon-critical as long as it is large enough to keep DC voltage ripple ata minimum. Bleeder resistor R1 with a value of 10 k to 100 k ohms isemployed to bleed off charge from C1 when the VLEG is desired to be off.Larger units would employ lower resistance bleeders. Circuit ground 137is connected to negative DC output terminal 129 and the positive DCvoltage appears through terminal 128. Note that the number of differentphase AC input power sources that can be accommodated by this circuit isnot subject to any limit; an n phase Schottky diode full wave bridgerectifier can be made up of n AC power inputs separated in phase by360°/n if 2n diodes are used, one pair of diodes for each additionalphase AC power input source. Also note that the AC power inputs do nothave to have any regular phase relationships to each other with thiscircuit. This characteristic as well as the use of Schottky diodes makesthis circuit particularly of use in harvesting electrical energy frommultiple parallel sources of voltages and currents of low magnitude andfrom four to thousands in number from sources of any vibrational energyincluding ocean surf, wind induced vibrations, transportation vehiclevibrations, and the like; the use of power Schottky barrier diodes suchas the 40 PIV 3A RK44 will enable the use of input sources ofconsiderable range of power magnitude.

The circuit 130 of FIG. 15D was designed for applications where it wouldbe desirable to have a bipolar output with a center tap ground. It toois a 4 phase full wave rectifier, but it is composed of two halfsections, each of which are full wave center tapped rectifier circuits;one section produces and separates out a positive half cycle pulse foreach phase resulting from four successive positive pulses from coils34-1 through 34-4 connected via leads AB, CD, EF, and HG respectivelythat are summed together by Schottky diodes D1 through D4 and filteredthrough large filter capacitor C1 into a positive DC voltage outputacross positive terminal 131 and circuit ground 132; the other sectionproduces and separates out a negative half cycle pulse for each phaseresulting in floor successive negative pulses from coils 34-1 through34-4 via leads AB, CD, EF, and GH respectively that are summed togetherby Schottky diodes D5 through D8 and filtered through large filtercapacitor C2 into a negative DC voltage output cross negative terminal133 and circuit ground 132. All capacitors for all of the exemplaryfiltering circuits to be described are as described for C1 for thecircuit of FIG. 15C. R1 and R2 are bleeder resistors with a preferredvalue of 10K to 100K. The positive 4 pulse train output 134 and thenegative 4 pulse train 135 developed as the PMA 37 N pole and then the Spole repulsive magnetic field regions of space around the rotor of theVLEG slides past FCA coils 34-1 through 34-4 in succession areillustrated in FIG. 15D. Some applications may require a bipolar outputwith a center tap neutral ground and circuitry that accomplishes thisdesired feature for 4-phase AC power lines to be rectified into abipolar DC power source with a center tap ground is believed to benovel. Distinguishing characteristics of this circuit include the use ofSchottky diodes and the use of full wave center tapped rectification foran AC power source of phase greater than three. This circuitconfiguration is believed to be quite novel and although the 4-phaseconfiguration is perfectly suitable for the exemplary embodiments of theVibrational Linear Energy Generator that forms the wave kinetic energydissipating electrical power generating capability of an EKS, thecircuit 130 can handle any number of coils, n, producing an n phases ACoutput that can be full wave rectified into a bipolar DC output withcenter tapped neutral ground through the addition of 2n additionaldiodes. Furthermore, note that the number of different phase AC inputpower sources that can be accommodated by this circuit is not subject toany limit; an n phase Schottky diode full wave bridge rectifier can bemade up of n AC power inputs separated in phase by 360°/n if 2n diodesare used, one pair of diodes for each additional phase AC power inputsource. The AC voltage inputs do not have to exhibit a constant phaserelationship to each other. This characteristic as well as use ofSchottky diodes makes this circuit particularly of use in harvestingelectrical energy vibrational energy sources other than ocean waves frommultiple parallel sources from four to thousands of voltages andcurrents of low magnitude; with the use of power Schottky diodes such asthe 40V PIV 3A RK44 used in exemplary embodiments described herein,these AC power sources can be considerable in terms of range ofmagnitude from very low to intermediate levels of power input.

Yet another Power Collecting Circuit that is advantageous with respectto configuration and function is denoted as a DC current summationcircuit and is illustrated in FIG. 15E as circuit 136. Here, each of thefour FCA coils 34-1 through 34-4 is connected by leads AB, CD, EH, andGH to Schottky diode full wave bridge rectifier circuits 136-1 through136-4 respectively; the bridge rectifier circuits are composed ofSchottky diodes D1-D4, D5-D8, D9-D12, and D13-D16 respectively. Theheavily rippled DC voltage output of each bridge rectifier is filteredby large filter capacitors C1 through C4 and, to bleed off residualcharge off these capacitors when the EKS apparatus is in the off state,bleed resistors R1 through R4 with a preferred value of 10K through 100Kare used. Using ballast or current balancing resistors R1 through R4 inseries with Schottky current steering diodes D17 through D20, the DCcurrent outputs from the four bridge rectifier circuits 136-1 through136-4 are summed together and connected to circuit ground via R5. R1through R4 are large power resistors with the same and extremely lowresistance of between 0.1 to 1.0 ohm as the preferred range and theratio of the load resistance that is placed between positive voltageoutput 140 and circuit ground 139 and any of the four current balancingballast resistors R1 through R4 should be smaller than the loadresistance by a factor of greater than 100 to 1 to minimize power lossesin the current balancing circuit. R5 is a bleeder resistor with thepreferred value of 10K to 100 k and C5 is an output filter of highcapacitance that filters the DC output voltage that appears acrosspositive terminal 140 and negative terminal 138 (circuit ground 138).Advantageous aspects of this circuit include: 1) Schottky diodes areused in the bridge rectifiers; 2) A current aggregating or summingcircuit is used to add together small to intermediate large currentoutflows from each of the 4 coils of the FCA of the VLEG through the useof ballast current balancing resistors which results in a higher voltageand current through any load resistance connected across outputterminals 139 and 140; 3) Schottky steering diodes insure that there isno DC current flowing backward into any of the coils if the outputfiltered DC voltage of one coil is less than that of another coil or ashort circuit/open circuit unstable condition occurs in any of the fourcoils. Note that the current balancing ballast resistors R1-R4 insurethat there are not different DC voltages present simultaneously from theoutputs of the four coils on the positive output terminal 140 whichwould be a highly undesirable situation. Note also that in the event ofa short circuit or open circuit of one of the coils, the steeringSchottky diodes D17 through D20 prevent undesirable current paths andunstable voltages from propagating through the other coils. Further,since the PCC 136 sums the output DC currents from each of the 4individual coils 34-1 through 34-4 into the output load resistance, thevoltage appearing across the load resistance across output terminals 39and 140 is the approximate sum of all 4 of the filtered DC outputvoltage from each coil. This higher load voltage is desirable inapplications where it is desired to minimize I squared R ohmic losses inthe transmission wires and allows better impedance matching and henceimproved power transfer efficiency as per the Maximum Power Theorembetween a higher resistance load and a lower resistance coil generatingelectrical power out. At the same time, if the load resistance isrequired to be small, the summation of the currents produced by the fourcoils through the load resistance is a desirable feature. Anotherdistinguishing feature of this circuit is that it may be used in anadvantageous manner of combining the current outputs of several VLEG'stogether as to be shortly described.

Another embodiment of a PCC in accordance with the present principles isshown in FIG. 15F, which depicts a voltage summation circuit 141. Thecircuit 141 includes a full wave bridge Schottky diode rectifier 141-1with diodes D1-D4 and large filter capacitor C1 whose AC voltage inputsare connected to the first coil 34-1 of the FCA via leads A and B andwhose DC voltage output is connected via Schottky diode D17 to thecircuit branch ground of the full wave bridge rectifying and filteringcircuit 141-2. The circuit 141-2 comprises Schottky diode bridge D5-D8with large filter capacitor C2 whose AC voltage inputs are connected tothe second coil 34-2 of the FCA via leads C and D and whose DC voltageoutput is connected via Schottky diode 18 to the circuit branch groundof the full wave bridge rectifying and filtering circuit 141-3. In turn,the circuit 141-3 comprises Schottky diode bridge D9-D12 with largefilter capacitor C3 whose AC Voltage inputs are connected to the thirdcoil 34-3 of the FCA via leads E and F and whose DC voltage output isconnected via Schottky diode D19 to the circuit branch ground of thefull wave bridge rectifying and filtering circuit 141-4. Further, thecircuit 141-4 comprises Schottky diode bridge D13-D16 with large filtercapacitor C4 whose AC voltage inputs are connected to the fourth coil34-4 via leads G and H and whose DC voltage output is connected viaSchottky diode D20 to the positive output terminal 143 via large filtercapacitor C5 and bleeder resistor R1. Here, the bleeder resistor R1 hasthe same purpose of bleeding off charge from the filter capacitor withthe same preferred resistance 10 K through 100K as in the previouslydescribed circuitry. The positive DC output voltage appears across thepositive terminal 143 and negative terminal 144 connected to circuitsystem ground 142 (which is identical to branch circuit ground 145-1).The magnitude of that DC voltage is the sum of the filtered output DCvoltages resulting from the induction of voltages in each of the coilsas PMA 37 slides past the four coils 34-1 to 34-4 in succession.Advantageous features of this circuit again include 1) Schottky diodebridge full wave circuitry 2) connected to each in series fashion to thenext one in sequence via Schottky steering diodes that prevent currentbackflow into each of the feeding coils, in essence isolating one coil'sDC voltage output from the other coils, thereby mitigating operatinginstabilities from possible short and open circuits that might occur inone of the coils and 3) combining output DC voltages of significantmagnitude together to produce the sum of the voltages produced by theindividual coils, a desired condition in applications where higheroutput voltages and lower output currents are required to decrease ohmicI squared R wire losses as well as when it is needed to more properlymatch a higher impedance load circuit to the lower impedance of thegenerating coils leading to more efficient power transfer as per theMaximum Power Theorem.

Note that any of the circuits of FIG. 15C, FIG. 15D, FIG. 15E, or FIG.15F may be used individually or in combination to form the PCC ofindividual VLEG's or groups of VLEG's that comprise the wave kineticenergy dissipation mechanism and electric power generation, and theexact selection and combination of these circuits that are used may varyas to the preferred embodiment with the structure of the VLEG matrixforming the WEC repeating component of the EKS and the number and shapeof the WEC array used in any given configuration in accordance with thepresent principles.

The current summing circuit 136 of FIG. 15E and the voltage summingcircuit 141 of FIG. 15F have some additional notable characteristics incommon. The number of AC power inputs, phased or unrelated in phase, maybe increased to any arbitrary number by adding additional full wavebridge rectifier filter circuits, and in the case of the current summingcircuit 136, additional Schottky current steering diodes and currentbalancing ballast resistors can be added in parallel; in the case of thevoltage summing circuit 141, additional rectified filtered DC outputscan be series connected as shown. Furthermore, the full wave bridgerectifier filter circuits in these power source summing circuits can bereplaced with direct DC voltage and current sources of any number, andthese input sources can be the DC outputs of circuits 127, 130, 136, and141 of FIG. 15C through FIG. 15F respectively or may represent any otherDC input power sources including batteries. The voltage and currentrating of the power Schottky barrier diodes used determine the magnitudeof the input DC power of the inputs that can be summed together. Onceagain, anywhere from three to thousands of AC power sources phased andnot in phase as well as DC power sources can be summated in an energyharvesting PCC from sources as diverse as ocean waves as in the case ofthe embodiments described herein, ocean surf, transportation relatedvibrational energy sources, and wind.

The significant flexibility of design for these four rectifying circuitslead to a complex and rich assortment of possible Power CollectionCircuitry configurations in accordance with the present principles, orfor that matter, any source of low level electrical energy, AC or DCpower, that is harvested from a great deal of energy collecting inputscovering an energy generating space. For instance, FIG. 16 shows a VLEG,drawn approximately to scale, comprising a PMA rotor with 4 structuralmagnetic units 153 containing central cavity 47 and metal support tube46; the PMA is in Compressive Repulsion Magnetic Field configuration anda FCA 150 with 32 separate coils of which 24 are shown; for simplicity,end deflecting magnetic field magnets are not shown. Output leads of the32 coils are organized in four banks of series connected coils so thatany coil in that group of 8 (5 coils in each group are actually shown tobe connected) is over the same magnetic pole region as the remainingcoils in that group causing the voltages induced in that coil to beadditive with the remaining seven coils; the input leads 151 to the 4banks of coils are designated A, C, E, and G; the output leads 152 fromthe 4 banks of coils are designated B, D, F, H. This configurationresults in the induced voltage and current in the first coil bank to be90 degrees ahead in phase of that induced in the second coil bank whichin turn is 90 degrees ahead in phase of the third coil bank which inturn is 90 degrees ahead of the fourth bank creating a four phase ACoutput across the corresponding pairs of input and output leads 151 and152. These input output lead pairs are designated AB, CD, EF, and GHwhich can then be fed to any of the 4 different types of PCC circuitsdepicted in: FIG. 15C, the Full Wave Schottky Diode Bridge RectifierFilter circuit 127; FIG. 15D, the Full Wave Schottky Diode Center TapRectifier Filter circuit with bipolar output and neutral center tap 130;FIG. 15E, the Current Summation Full Wave Schottky Diode BridgeRectifier Filter circuit 136; and FIG. 15F, the Voltage Summation FullWave Schottky Diode Bridge Rectifier Filter circuit 141. Input outputlead pairs AB, CD, EF, and GH correspond to the lead connections of the4 coils of the four PCC circuits of FIG. 15 labeled in the identicalmanner. From any of these four PCC circuits, the generated electricalpower can be then taken off the WEC and EKS directly as shown by theblock diagram in FIG. 14, stored in a storage battery, converted to adifferent DC voltage via a DC to DC converter 148 or changed to asuitable alternative AC voltage by a DC to AC inverter 148A.

FIG. 17 depicts a different exemplary configuration for the PCC of theWEC repeating unit of an exemplary EKS apparatus. PMA rotor 154, drawnapproximately to scale, comprises 3 VLEG magnetic structural units 153in Compression Repulsive Magnetic Field configuration again with centralchannel 47 through which central support metal tube 46 travels; forsimplicity, end deflecting magnetic field magnets are not shown. FCA 150comprises 24 coils grouped in groups of 4 coils that are alignedadjacent to each other with one group extending the length of one VLEGPMA magnetic structural unit as previously described. Each group of 4coils are assigned a number 1 through 6 and for each group of coils,four pairs of leads emanate, one from each coil; from the first coilthey are labeled as 1A and 1B, 1C and 1D, 1E and 1F, 1G and 1H; from thesecond coil they are labeled as 2A and 2B, 2C and 2D, 2E and 2F, 2G and2H; and so on for all 6 coil groups of 4. The leads from a numberedgroup of 4 coils go to a respectively numbered four phase full waveSchottky diode rectifier and filter circuit 127 that has been previouslydescribed. Again the lettering code of the leads matches up with thecoil connections of the rectifier circuit 127 of FIG. 15C. Again theoutput of each coil of the coil group differs in phase by 90 degreesfrom the coil adjacent to it to produce a 4 phase AC power signal thatwill be rectified by the numbered four phase rectifier filter circuit127 associated with that numbered coil group. These rectifier circuits127 numbered as 127-1 through 127-6 each produce a pair of positive andnegative DC voltage and current output pairs designated as 1+ and 1−, 2+and 2−, and so forth through 6+ and 6−. We now have six separate DCvoltage current sources emanating from the six rectifier circuits. Sincethe desired goal is to combine all 6 DC power lines into one stable DCoutput power line that has collected the power from all the coils in theVLEG, we can use, for example, either a novel 6 input current summationcircuit 155 or novel six input voltage summation circuit 156 toaccomplish the corresponding design. Only two pairs of output leads fromtwo of the four 4-phase rectifier circuits are shown for the sake ofclarity connected to either the current summing circuit 155 or thevoltage summing circuit 156. Obviously, all six pairs of outputs fromthe six rectifier circuits 127-1 through 127-6 would be connected to acircuit 155 or 156.

It is important to note that in fact the full wave Schottky diode bridgerectifier circuit 127 could have easily been replaced with any of theother three circuits 130, 136, and 141 of FIG. 15D, FIGS. 15E and 15Frespectively; for circuit 130 the center tapped ground of the bipolar DCoutput would not be used in this case, in effect creating a voltagedoubling circuit across the positive and negative outputs; circuit 136would sum all the DC currents produced from each of the 4 coils in eachVLEG unit; circuit 141 would sum all the DC voltages produced from eachof the 4 coils in the VLEG unit. The final DC voltage and current outputof the PCC would vary depending on which of the four circuits processedthe AC power generated by the six groups of 4 coils and fed theiroutputs to either circuit 155 or 156 of FIG. 17, but the maximum totalDC power output possible with appropriate load circuits would beapproximately the same for a given quantity of wave input energy aswould be expected as that parameter only depends upon the electricalcharacteristics of the VLEG itself.

The electronic details of six input current summation circuit 155 andsix input voltage summation circuit 156 depicted in FIG. 17 areillustrated in FIG. 18A and FIG. 18B respectively. In FIG. 18A, all 6input pairs from the six 4-phase rectifier filter circuits 127-1 to127-6 are directed in such a way that the negative inputs are groundedto circuit ground 162 and the positive inputs are directed throughcurrent directing Schottky diodes 158 D1-D6 via current balancingballast resistors R1-R6 to the positive DC voltage output 162A. TheSchottky diodes serve the function of preventing any back flow ofcurrent to any of the six 4-phase rectifier outputs if suddenly thevoltage on one input line exceeded the voltage on another input linewhich would, without the diode, cause current to flow from the highervoltage input line into the lower voltage input line, that is back intothe output of the 4-phase rectifier that had an instantaneous lowervoltage output then another 4-phase rectifier. This would create highlyunstable electrical currents in the output sections of the circuitrycausing an undesirable and possibly even dangerous effect. Also, in theevent that a coil or one of the 4-phase rectifiers develops a short,there would not be a massive inrush of current into the shorted input orcoil, and if one coil or 4-phase rectifier circuit developed an opencircuit, a large voltage would not be directed backwards to otherportions of the PCC. The current summing function is carried out byballast resistors R1 through R6 whose current balancing ensures that thevoltage is constant at the same level at all points on the positivevoltage output bus. C1 165 is a large filter capacitor of at least10,000 microfarads to decrease DC ripple, and R7 is a bleeder resistorof 1K to 10K that discharges C1 after the EKS is turned off formaintenance purposes, but it should be a power resistor as the residualcharge is much larger than with previous PCC examples already shown. Thecurrent delivered to the load resistance (not shown) is equal to the sumof the currents in the 6 input lines from the six rectifier circuits127-1 through 127-6 and the measured voltage across the load resistanceis approximately somewhat less than the sum of the instantaneouspositive DC voltages on all of the input lines. Essentially six DCcurrent sources are being connected in parallel into the loadresistance. Note that this circuit is essentially a six input version ofcircuit 136 of FIG. 15E with the bridge rectifier filter sub-circuitsfrom the input coils being replaced by the DC output voltages from thesix rectifier circuits 127-1 through 127-6.

FIG. 18B illustrates a six input voltage summation circuit 156 ingreater detail and it is essentially circuit 141 shown in FIG. 15F butnow there are 6 DC input pairs from the six 4-phase Schottky diode fullwave bridge rectifier filter circuits 127-1 through 127-6 instead of the4 AC voltage inputs from the coils and their full wave bridge rectifierfilter sub-circuits. The negative inputs of each input pair is connecteddirectly to a local input ground 161-1 through 161-6, respectively. Thepositive input of input pair 1 from rectifier circuit 127-1 is connectedto the local input ground 161-2 via Schottky diode D1, the positiveinput of input pair 2 from rectifier 127-2 is connected to the localinput ground 161-3, via D2, the positive input of input pair 3 fromrectifier 127-3 is connected to the local input ground 161-4 via D3, thepositive input of input pair 4 from rectifier 127-4 is connected to thelocal input ground 161-5 via D4, the positive input of input pair 5 fromrectifier 127-5 is connected to the local input ground 161-6 via D5 andthe positive input of input pair 6 is connected directly to the positiveoutput bus 163A via D6. The positive DC output voltage appears betweencircuit ground 162 that is tied to local ground 161-1 and the positiveoutput terminal 162A and it is a sum of the instantaneous voltagespresent at any given time on the six positive input lines disregardingthe tiny voltage drops across the Schottky diode junctions. Essentially,six DC voltage sources are being connected in series into the loadresistance. Once again, capacitor C1 165 is large in excess of 10,000microfarads and provides additional DC voltage filtering, and R1 is ableeder power resistor of 1K to 10K draining charge from C1 when theapparatus is shut down for maintenance or other reasons.

Note that the six input current summation circuit 155 is a six inputextension of the previously discussed four input current summationcircuit 136 of FIG. 15E and the six input voltage summation circuit 156is a six input extension of the previously discussed four input voltagesummation circuit 141 of FIG. 15F. Note also, whereas the inputs to thecircuits 136 and 141 of FIG. 15 E and FIG. 15F respectively were coiloutputs, the inputs in the embodiment of the PCC of FIG. 17 are the DCoutputs of a group of four phase AC full wave Schottky diode bridgerectifiers. Note further that input extensions of circuits 136 and 141allow for any group of DC currents and voltages to be summed togetherinto one current and voltage output source respectively and these inputscan be not only DC voltage and current outputs from any of the fourcircuits depicted in FIG. 15C through FIG. 15F, but any DC inputs ofreasonable voltage and current from many types of electrical sourcesincluding batteries. Hence the configuration pattern potential of thePower Collection Circuitry embodiments of the present principles isremarkably robust and yet remarkably simple in configuration andadvantageously combine DC input power sources in parallel into oneoutput power source. Further, the embodiments of the present principlesdescribed herein are applied for the aggregation and energy harvestingof multiple parallel low and intermediate DC input power sources to asingle DC output power source. The circuitry described herein isuniquely suitable and advantageous for dissipating wave kinetic energyby a large number of WEC repeating units of EKS apparatuses. However, itshould be understood that this energy harvesting circuitry is by allmeans not limited to the application described herein. Indeed, anygeometrical array of vibrational energy over a spatial region such aspiezoelectrical generators, radiofrequency antenna receiver generators,geothermal thermoelectric generators and so forth using physicalprinciples that are different from Faraday's law that underlies thefunctioning of the embodiments of the present principles describedherein can be inputted into circuits 127, 130, 136, and 141 and networksof such circuits to allow for aggregation of low and intermediate levelvibrational power sources into useable electric energy present withinthe confines of that space.

One other distinct advantage of circuits 127, 130, 136, and 141 is thatthe outputs of these circuits themselves can be used to fine tune andadjust the maximum output of the WEC VLEG. These circuits present aneffective load resistance between their DC voltage outputs to thecomplexly wired FCA of the armature of the VLEG. This load resistance ismostly governed by what is connected to these outputs but also isaffected by the PCC circuits themselves. The load resistance can beoptimized for the effective coil resistance represented by the networkof FCA coils even after all of the design parameters of the VLEG hasbeen set by installing a monolithic switching DC to DC converter 148 ofFIG. 18C across the DC outputs of the above-described circuits such hasbeen done with the working prototypes of the present principles. Byadjusting the output voltage of the converter, the effective loadresistance facing the generator coils can be adjusted so that theeffective load and coil resistances are approximately equal to eachother, satisfying the maximal power transfer theorem, and theelectromagnetic damping can be made approximately equal to the parasiticdamping of the generator. This fine tuning of the VLEG power output thushelps achieve two conditions: 1) maximum efficiency of energytransferred to the load and 2) maximum power generated by the generator.The series of monolithic regulating converters by Dimension Engineering™(DE-SWADJ3 (5-35V in, 3-13V out, 3A out) and DE-SWADJHV (5-60V in, 2-14Vout, 1A out) are quite but not uniquely suitable for this application asthey are >95% efficient, extremely and precisely adjustable, and may beplaced in parallel for greater power handling ability. Placed in betweenthe power collection circuits 127, 130, 136, and 141, and the loaddestination of the WEC, this component allows input wave kinetic energyto be dissipated to its maximum extent with all other variables heldconstant yielding the maximum amount of electrical power across the loadwith little loss of power in the converter.

FIG. 18C illustrates that the DC output may be changed to a different DCvoltage through DC-to-DC converter 148 or to AC of a desired voltagethrough DC-to-AC inverter 167.

FIG. 18D shows an unique ultra-precise configuration 155 a of the 6input current summation circuit 155 (FIG. 18A) version of circuit 136 inwhich the monolithic DC to DC circuit 148 (DC-1 thru DC-6) describedabove is placed in series after the current steering Schottky diodes 158(D1-D6) and in series before a second set of current steering diodes 158a (D7-D12) placed in series with the current balancing ballast resistor159 in each of the six circuit branches. Diodes 158 perform at leastthree functions—1) isolation of the DC inputs 1 through 6, 2) protectionagainst short circuits and open circuits in the DC inputs, and 3)blockage of any reverse flowing currents back to the DC inputs. Diodes158 a perform at least four functions—1) isolation of the DC to DCconverter outputs from each other, 2) protection against short circuitsand open circuits in the DC to DC converter outputs, 3) blockage of anyreverse flowing currents back into the DC to DC converters and 4)precise equalization of the voltage outputs at the junction of thediodes D7-D12 and the ballast current balancing resistors by precisemanual adjustment of the converter output voltage, an inherent featureof the ten turn precision miniature potentiometer that is an integralpart of these monolithic regulating switching converters by DimensionEngineering™, which reduces the ohmic losses in these resistors as theyfurther equalize the voltage at all points on the positive DC output bus162 a. The fourth-described function of diodes 158 a is accomplishedprecisely in this embodiment by the 10 turn voltage adjust control 148 aon each DC to DC converter DC1 through DC6 which serves to preciselyadjust the effective output load resistance presented to the FCA coilsand it is this feature that gives this exemplary circuit such precisionand reliability to summate a large number of parallel DC power inputcurrents together into one stable DC output current with the maximumefficiency subject to the constraints of the Maximum Power Theorem.Diodes 158 a (D7-D12) should be matched as closely as possible withrespect to the voltage drop across their barrier junctions to accomplishthis precise voltage equalization in the most effective manner; diodes158 (D1-D6) do not have to be closely matched in the just describedmanner. Ballast resistors 159 (R1-R6), filter capacitor 165 (C1) andbleeder resistor 164 (R7) are as and function as previously described incircuit 157.

Of the power collection circuits 127, 130, 136, and 141, the currentsummation circuit 136 derives the most significantly advantageousperformance from the configuration 155 a of placing the DC to DCswitching regulator converter 148 after each steering diode 158. In thissix input configuration 155 a variation of circuit 136, the outputvoltage at the junction of the positive output terminal of 148 andcurrent balancing ballast resistor 159 can be balanced extremelyprecisely so that the six branch circuit voltage outputs are preciselyequal at these junctions so that the ballast resistors can much moreefficiently keep all points of the positive output circuit bus preciselyat the same voltage. This in turn reduces power consumption of theballast resistors and can more precisely balance the effective outputresistance presented to the generator armature coils or to prior PCCcircuits used in the power collection circuitry. It is important to notethat this circuit allows for the use of batteries and other DC inputsources that may be of different voltages to have their current inputssummed in parallel to one final summation output current with extremeconstant precision and reliability against voltage and current outputvariations, shorts and open circuits in the input DC sources.Furthermore if one or more of the parallel DC input voltages drift inmagnitude over time, the output DC voltage of circuit 157 will holdprecisely steady. Thus, the parallel DC output currents of several WECrepeating units of the EKS may be combined together into one electricalcable using this preferred type of circuitry represented byconfiguration 155 a if ultra precise and reliable current summation isdesired. For power collection circuitry of individual coils in the FCAof individual VLEG's that would not ordinarily require the ultra preciseversion 155 a of circuit 136, the circuit configuration of 136 in FIG.15E would suffice. It is believed that this given configuration ofcurrent summation circuitry is a novel way of combining parallel DCinput currents into a single summed output current. Note that the 4terminal monolithic switching regulator DC to DC converter 148 employedhere has only two input leads with one connected to circuit ground 162,and two output leads with one connected to circuit ground 162, givingthis circuit tremendous simplicity. Furthermore, since each DimensionEngineering™ converter can handle an input DC voltage and current of 25w, the six such inputs can be summed together to yield an outputsummation current that can be as high as 150 watts across the loadbetween outputs 162 and 162 a. The number of inputs as in the case ofthe other circuits can be extended to as many as desired simply byadding the corresponding identical components to additional identicalbranches for additional power output. Similarly suitable DC to DCconverters of similar or higher power handling capacity may besubstituted for the Dimension Engineering™ component used in theexemplary embodiments described here, though this switching regulatingDC to DC converter is the preferred converter so chosen because of itsmonolithic compact structural form, its extremely high efficiency, theprecise multi-turn potentiometer, its wide range of input and output DCvoltages, stability, and its ability to have multiple such devices inparallel to handle even significantly more powerful DC input voltagesources. Such versatility, simplicity, precision, and power handlingcapacity for the art of summation of parallel low and intermediatemagnitude sized DC currents to produce one summation output current inthe configurations described herein is believed to be novel.

FIG. 19 is a further demonstration of the versatility of the PCCcircuitry described in FIGS. 15 C, D, E, and F or FIGS. 16, 17, 18A, B,and D. FIG. 19A represents three separate VLEG units of order 3 (3 PMAstructural magnetic units) in three separate WEC repeating components168, 169, and 170 of a small three-WEC linear array EKS apparatus eachcontaining a PMA rotor structure, a FCA stator structure, and a PCCwhose output paired sets of positive and negative terminals are given by171, 172, 173 with the individual output lines being given as 1− and 1+,2− and 2+, 3− and 3+ respectively; each WEC has its own ground 177 goingto circuits 175 and 176 as lines 1−, 2−, and 3−; the PCC for each VLEGof each WEC can be any of the PCC embodiments in FIGS. 15 C, D, E, and For FIG. 16, FIG. 17, FIGS. 18A, B, and D. FIG. 19B represents circuit175, a three input embodiment of the current summation circuit 136 ofFIG. 15E with 3 sets of DC voltage inputs 174A from WEC's 168, 169, and170, and FIG. 19C represents circuit 176, a three input embodiment ofthe voltage summation circuit 141 of FIG. 15F with 3 sets of DC voltageinputs 174B from WEC's 168, 169, and 170; all current balancing ballastresistors 183 (R2-R4), both filtering capacitors 181, (C1), and 182,(C2), respectively, and bleeder resistors 184, (R1), and 185, (R2), aswell as current steering Schottky diodes 179 (D1-D3) for currentsummation circuit 175 and 180 (D4-D6) for voltage summation circuit 176have the functions ascribed to them previously; 178 represents the inputgrounds (1−, 2−, 3−) to the current summation circuit 175; input DCvoltage and current inputs 174B (1+, 2+, 3+), system grounds 189 andlocal grounds 186, 187, 188 are present for the voltage summationcircuit as in previous circuit embodiments; output DC line pair 190 ofthe current summation circuit and output DC line pair 190A of thevoltage summation circuit represent the final power output collectionpoint of all of the 3 VLEG's in the 3 WEC's comprising a 3 WEC array ofthe present invention. Note that the 3 input version of circuit 155 a ofFIG. 18D representing the enhanced current summation circuitry can besubstituted for current summation circuit 175 of FIG. 19B for enhancedreliability at the point of the final power output stage of the PCC forthe array of WEC repeating units of the EKS. From that power collectionpoint 190 or 190A of the entire PCC for the EKS apparatus, all of theavailable generated electrical power of the EKS apparatus is directed toa load application located on or off the EKS apparatus or both, abattery for energy storage, a DC to AC inverter, or another DC to DCconverter for any output DC voltage that may be desired as well as powerfor illuminating the EKS apparatus at night and the video monitoringsystem. The PCC of either FIG. 19B or 19C can be extended to any numberof DC input pairs from any number of VLEG's in any number of WEC's ofany EKS apparatus of any shape, dimension, or geometric configuration.

Wave Energy Dissipation and Electrical Power Generation Parameters

FIG. 20A shows the exponential square relationship of the incident powerper meter of wave front of the waves impinging upon an EKS apparatus asa function of the significant wave height which is defined as theaverage statistical height of the highest one third of all wave heightsthat occur in a defined observed period of time. FIG. 20B shows thelinear relationship between the incident power per meter wave front as afunction of wave period. FIG. 20C displays the electrical powerdeveloped in the VLEG as a function of the product of the magnetcylinder diameter squared and magnet thickness and varies as a functionof the cube of the linear dimensions of the magnets used in the rotorassuming the strength of the magnetization strength of each of themagnetic material is held constant. FIG. 20D shows that the electricpower developed in the VLEG's is linearly related to the number of thebasic VLEG structural magnetic units in the PMA. FIG. 20E shows that theelectrical power developed for a given sized LEG is proportional in alinear manner to the N magnetization factor of the magnet which rangesfrom 0 (non-magnetized) to N52, the strongest NIB (NdFeB) rare earthmagnets currently available commercially. FIG. 20F shows the peakelectrical power developed by a VLEG consisting of one PMA of nstructural magnetic units and 3n groups of 4 coils and it isproportional to n squared.

FIG. 21 shows the phase relationship between the wave force in on theWEC repeating component of an EKS and the velocity of the rotor; whilethe velocity of the rotor is in phase with the wave force on the WEC,the displacement of the rotor lags these two parameters by 90 degrees.The voltage developed in the FCA by the PMA is dependent on 4 temporalfactors: 1) dependence upon the frequency of the modulated sine wavepattern of the wave input force; 2) the pole pitch, that is the distancebetween adjacent regions of repulsive magnetic fields and the endmagnetic pole fields from the nearest repulsive magnetic region and thisis dependent upon the thickness of the magnets and pole pieces used; 3)the frequency of the AC voltage generated in each coil equals the numberof alternating polarity magnetic field region pairs that passes throughthat coil per unit time; 4) the summation of all the voltages generatedin all the coils of the FCA at any point in time. Note that the periodand shape of the waves impinging upon the EKS apparatus modulates anddetermines the shape of the complex voltage waveform produced by theother three factors. Finally, a graph of watts (P_(M)) developed in therotor as kinetic energy, which can be shown to be equal to the productof the instantaneous value for the wave force in (F_(in)) on the WEC andthe rotor's velocity (V_(R)), can be shown to be related to theelectrical watts generated in each coil which is a product of thevoltage generated in each coil and the current generated in each coil;for the entire VLEG, the electrical power generated=the product of theproduced generator voltage and current, that is, P_(E)=(E_(gen))(I_(gen)) and P_(E) is related to the load resistance whereP_(E)=(E_(gen))²/R_(L).

Efficiency of the EKS Apparatus

The wave kinetic energy that is dissipated by the EKS apparatus and theresulting electrical power generated is dependent in a complicatedmanner on parameters that are either external to the EKS apparatus andcharacteristic of the ocean wave environment or parameters that areinternal to the design and structure of the EKS apparatus itself.External factors include: the mechanical impedance matching between theEKS and the impinging waves; the period of the incident ocean waves (L);the depth of the ocean where the EKS apparatus is in place; the angle ofwave incidence relative to the EKS apparatus (not applicable toomni-directional circular or near circular geometric mesh EKS arrays);the number of rows of WEC repeating components of the EKS apparatus, thegeometry of the WEC array, the total number of WEC's, and the force in(F_(in)) exerted by the incident ocean waves dependent both as asinusoidal or approximately sinusoidal function of time and a quantitythat is a product of the significant height (H_(te)) previously definedof the incident ocean waves, the depth constant (δ), the cross sectionalarea of the buoy floatation collar of the mobile subunit (A), thedensity of water ρ, and the gravity acceleration, g; internal parametersof an electromagnetic or mechanical nature which affects the generatorcharacteristic of electromagnetic damping, which include: thecharacteristics of the spring suspension system including springconstants; the structural shape, cross sectional buoyant area (A), andmass magnitude of the fixed and mobile subunits; compressed repulsivemagnetic field PMA magnet shape, size, magnetization strength, and therepulsive pole inter-pole distance; FCA shape geometry, diameter andthickness of the coils, number of coils, wire gauge; magnetic fluxleakage loss, hysteresis losses, eddy losses, and Lenz's Law losses;Ohmic resistance losses of the coil windings; diode junction voltagedrops of the power collection circuitry; mass of the rotor; length ofthe rotor with respect to the length of the stator, the stroke volumetraveled by the rotor and its relation to the significant height of theincident ocean waves, and the maximum velocity of the rotor relative tothe stator; the structural geometric characteristics or order (orderequals the product of the rows of PMA's, the number of magnetic units ineach PMA, and the number of layers of PMA's) of the ElectrokineticTransducer used in the VLEG of the WEC repeating component; the fluxgradient along the axis of vibration of the rotor; and air gap betweenthe rotor and stator. Internal factors of a mechanical energy wastagenature which comprise the generator parameter known as parasitic dampinginclude: frictional sliding losses of the rotor, air resistance to rotormovement, thermoelastic losses in the springs, and unwanted oscillationof the fixed subunit in response to the input wave. The presentprinciples have dealt with ways to optimize all of these factors toenhance the performance of the exemplary embodiments disclosed herein.

All electrical generators, rotary and linear alike, have theirelectrical generation output affected by two parameters characteristicof every such generator, the electrical (voltage) constant (K_(E)) andthe force constant (K_(F)). The force constant, K_(F), is dependent uponthe design and geometry of the generator and it is the proportionalityconstant in the Lenz's Law counter EMF force that attempts to oppose therotor's velocity and acceleration and is given byF_(leg)=(K_(F))(I_(gen)), where F_(leg) equals the back EMF force on therotor and I_(gen) equals the current developed in the field coils of thegenerator. The electrical constant, K_(E), is dependent upon such thingsas magnetic pole to field coil air gap, the geometry of the magneticfield, the geometry of the coil assembly of the generator, the armatureconcentration (which in the exemplary embodiments described herein isimplemented by magnetic flux focusing by a repulsive field poleconfiguration rather than through the use of heavy ferromagneticarmatures) and the flux density of the magnetic field. It is related tothe electromagnetic damping factor already discussed.

In order to discuss power output, it is necessary to refer to theequation of motion of VLEG embodiments of the present principles. Inwords, it can be stated that the wave force in (F_(in)) on the WECmobile subunit is equal to the sum of the counteracting force of themobile subunit (F_(MSU), equal to the product of the mass of the waterdisplaced by the mobile subunit and its acceleration or rate of changeof its velocity, dv_(pma)/dt) plus the opposing force to due Lenz's Lawcounter EMF, F_(L), opposing the motion of the rotor. In mathematicalterms, this may be written as equation 8:

F _(IN) =F _(MSU) +F _(L) where F _(IN)=0.5 ρgAH _(te)δ sin(ωt),F _(MSU)=ρAL(dv _(pma) /dt),F _(L) =K _(F) K _(E) v _(pma) /R _(L)

and the mass of the water displaced by the mobile subunit=the mass ofthe subunit, and the velocity of the rotor PMA (v_(pma))) equals thevelocity of the mobile subunit induced by the wave. This gives us thesecond order differential equation of motion for the VLEG:

0.5 ρgAH _(TE)δ sin(ωt)=ρAL(dv _(pma) /dt)+K _(F) K _(E) v _(pma) /R_(L)  Eq. 8:

which when solved for the displacement of the mobile subunit (and rotor)with respect to time, thereby allowing the derivation for the equationfor the peak and instantaneous power of the wave driven verticaloscillation of the rotor relative to the stator of the VLEG, it can thenbe shown that:

P _(Out)=(F _(IN) K _(E))² R _(L)/2[(K _(F) K _(E))²+(ωR _(L)ρAL)²]  Eq. 9A:

P _(Peak)=(ρgAH _(te) δK _(E))² R _(L)/8[(K _(F) K _(E))²+(ωR _(L)ρAL)²]  Eq. 9B:

P _(Out) =P _(Peak)(sin ωt)²  Eq. 9C:

where P_(out)=the instantaneous power output of the VLEG in watts whichwhen integrated over time will yield the average power out, P_(Peak)=thepeak power output in watts, R_(L)=the load resistance in ohms, ρ=thedensity of water in kg/m³, g=the gravitational acceleration in m/s²,A=the cross-sectional area of the oscillating subunit of the WECrepeating component of the corresponding EKS, the buoy floatationcollar, which is exposed to the buoyant force of the incoming wave,H_(te) is the significant wave height, δ=a constant (depth constant)derived from the wave equation using the wave period, L, of the wave anddepth of the ocean at that point and it decreases with depth, ω=2π/T_(e)where ω and T_(e) is the angular frequency and period of the waverespectively, K_(F) and K_(E) are the force and electrical constants ofthe generator, L is the depth the buoy floatation collar of the fixedsubunit is submerged beneath the ocean surface, F_(IN) is the wave forceexerted by the wave on the buoy floatation collar and is given byequation 8 and its associated equations above, and s_(r) is equal to therotor stroke length. If we assume that for the basic VLEG of a givensize including a PMA having one magnetic structural unit consisting oftwo magnets in repulsive magnetic field configuration and twoferromagnetic pole pieces (an end pole piece and an interior repulsivefield pole piece) plus one additional end pole piece and an FCA having 4field coils whose width is approximately one quarter of the length ofthe cylinder formed by the magnetic structural unit as the preferred butnot exclusive arrangement, K_(F) and K_(E) will have a constant valuefor every similarly designed and similarly sized basic VLEG unit. Ifeach WEC is composed of a VLEG electrokinetic matrix transducer of orderN where N is defined as previously,

N=(2x+1)(y)(2z+1),integers x and z>=0,y>=1,

where N=the order of the VLEG Electrokinetic Transducer matrix equal tothe product of the number of structural magnetic units in each PMA, thenumber of PMA's in each layer of PMA's, and the number of layers in eachtransducer matrix with the basic VLEG unit being of order 1, and giventhat there is one Transducer Matrix in each WEC repeating unit of theEKS apparatus in this example, and M is the number of WEC's in the EKSarray apparatus, the instantaneous and Peak power generated for M suchtransducers in M WEC repeating components of the EKS is:

P _(Out)=(N M)P _(Peak)(sin ωt)² where P _(Peak) is defined by Eq. 9Babove.  Eq. 10:

When we examine these equations, we see that the wave kinetic energydissipation function will be optimized and electrical output power ofthe generator will increase and can be maximized by reducing generatorconstants K_(F), K_(E) by design adjustments to the internal parameterslisted above, by adjusting the effective load resistance R_(L) to equalthe combined FCA generator resistance of each repeating component of theentire EKS apparatus as per the Maximum Power Theorem, by making A aslarge as possible and L as small as possible by design adjustments tothe external parameters listed above and causing the mobile subunit tofloat as close to the ocean surface as possible where the greatest waveforce and energy flow occurs, and by placement of the EKS apparatus inthe ocean or any suitable body of water at a location having appropriatepropagating waves of significant height subject to the maximum waveheight and period consistent with the design considerations relatingendurance and structural strength of the WEC repeating components.Making the submerged depth of the buoy floatation collar, L_(wec), aslow as possible is advantageous, and should be done so by significantlydecreasing its mass, (mass (2)) which along with the mass of the rotor(M3) should be small relative to the fixed subunit mass (1) and thus, L,should be very small relative to the height of the buoy floatationcollar which should be greater than s_(r), the maximum rotor strokedistance; nevertheless, for every small decrement in depth that the buoyfloatation collar can be submerged and placed closer to the oceansurface, the greater the force and hence the greater the kinetic energythat will be imparted advantageously to the rotor. This can be done bymeans of adjustment of the amount, shape, and volume of the buoyancymaterial keeping the buoyancy floatation collar afloat. A significantportion of the mass of the mobile subunit, which consists of the mass ofthe buoy floatation collar (M2) plus the mass of the rotor (M3), shouldreside in the rotor because, for a given wave height, the maximumkinetic energy developed in the rotor depends on its mass as well as thesquare of its developed velocity in response to the acceleration by thewave.

Efficiency of an EKS apparatus in dissipating ocean wave kinetic energycan be defined by the output amount of electrical power extracted by theEKS divided by the power in the wavefronts impinging upon the entire EKSacross the line of intersection between the entire EKS covering acertain area of wave surface corrected in some cases for the angle ofwave propagation. The first quantity is given by equation (8) above andthe second quantity is given either equation (1) or its approximation,equation (2). However, since the WEC repeating components should bespaced apart in the water, much of the wavefront does not intersect aWEC and simply passes through it undisturbed. Furthermore, the fact thatthere may be multiple rows of WEC's and a wide variety of geometricshapes to the EKS, computing efficiency on this basis would bedifficult.

A better procedure would be to define six possible efficiencies: first,the efficiency of conversion of electrical energy (or power) from thewave kinetic energy captured by the EKS array as a whole may be definedas the ratio of electrical power produced by the array to the wavekinetic energy (or power) incident upon the array. Second, theefficiency of each WEC repeating unit may be defined as the ratio of theamount of electrical energy (or power) produced by one WEC to the amountof kinetic energy (or power) incident upon that WEC. Obviously, thefirst efficiency will always be less than the second, as there areregions of space within the EKS array where the wave passes throughundisturbed. Third, the efficiency of each WEC for the dissipation ofkinetic wave energy (or power) impinging upon that WEC may be defined asthe ratio of the wave kinetic energy (or power) captured by that WEC tothe wave kinetic energy (or power) incident upon that WEC. Fourth, theefficiency of the entire EKS in dissipating wave kinetic energy may bedefined as the ratio of the captured kinetic energy (or power) of allthe WEC's together to the ratio of the incident wave kinetic energy (orpower) upon the entire EKS array. Fifth, we may define the efficiency ofthe electrical energy (or power) conversion of the kinetic energycaptured by each WEC as the ratio of the electrical energy (or power)output by that WEC to the kinetic energy (or power) captured by thatWEC. Sixth, and finally, we may define the efficiency of the electricalenergy (or power) conversion of the kinetic energy captured by the EKSarray in its entirety by the ratio of the electrical energy generated bythe array to the total amount of wave kinetic energy captured anddissipated by the array. As opposed to giving a detailed account of howto measure and calculate these six efficiencies, for purposes ofbrevity, a sample calculation for the first two efficiencies in anidealized simplified manner is provided:

1) First measure the maximum electrical power generated by all of theWEC repeating components together, that is the total electrical powergenerated by the EKS apparatus that is extractable to a load circuitwhose resistance most closely matches the combined internal resistanceof all the coil windings in all the FCA armatures in all the WECrepeating units in the EKS. This is P_(ext). Then 2P_(ext) will be thetotal amount of electrical power generated including the 50% lost in thecoil windings as per the maximal power transfer theorem. To compute thisload resistance matching the internal resistance of the EKS, compute ormeasure it for one WEC unit, and then calculate the parallel resistancefor all the WEC units together. One can also vary the load resistance ofthe EKS array and determine the maximal power output, known as theMaximal Power Point (MPP) for the WEC array. Once this measurement isobtained, using the Maximal Power Theorem, double this measuredelectrical power output to produce the total amount of electrical powerproduced in the EKS including the 50% I squared R ohmic losses in thecoil windings. This will also give 2P_(ext). 2P_(ext) can also beobtained by measuring the maximum electrical output with a loadimpedance (resistance) matched for a single WEC, doubling that value,multiplying by the number of WEC's in the EKS; this is accurate if eachWEC sees waves of approximately the same amplitude. However, for an EKSarray with many parallel rows, the incident wave power and energypresented to any WEC will vary with the row that the WEC is located andhence the electrical output power will vary somewhat, and thecalculations will be more complex. Note also that the Maximal PowerTheorem really refers to impedance matching, but since the frequency ofthe AC power produced is so low given the low wave frequency, theimpedance matching refers to load resistance matching with the EKS's FCAcoil windings and the effects of inductance and capacitance can belargely ignored in this situation.2) Next compute the Power Extracted. P_(ext), for each WEC by dividingP_(ext) by the number of WEC repeating units in the EKS array.3) Determine the length of the line of intersection between the base ofthe floatation collar and the incoming wavefront. Since the WEC mobilesubunit floatation collar is a round structure, one does not have tocorrect for the angle of incidence of the waves onto the WEC.4) Compute the wave energy flux or wave power in w/m of wave frontimpinging on the WEC by using either equation 1 or its approximationequation 2 to compute the wave energy flux for the ocean around the WECin w/m and then multiplying this quantity of power in w/m of wavefrontby the length of the line of intersection of the mobile subunitfloatation collar base with the impinging wave front. This is theaverage input wave power for each WEC.5) Divide the quantity in step 2 by step 4 to give the efficiency of theconversion of incident wave kinetic energy to electrical energy by eachWEC as defined by efficiency definition number two above.6) Compute the total incident wave power that impinges upon the entireEKS array. First determine the widest cross section diameter of the areaof ocean covered by the EKS array that is in a direction perpendicularto the direction of wave propagation. Then determine the wave power orwave energy flux that is present in the wavefront impinging thatcross-sectional diameter to give the amount of wave power impinging uponthe entire EKS array in KW/m using eq. 1 or its approximation eq. 2.7) Divide the quantity 2P_(ext) of step 1, the total electrical powergenerated by the EKS array, by the total wave power incident on theentire EKS array calculated in step 6 to give the efficiency ofelectrical conversion as defined by efficiency definition number oneabove for the entire EKS array as a whole.

Note that these calculations can be done using either wave kineticenergy (J/m² of ocean surface) or wave energy flux (wave power) (w/m ofincident wave front) and electrical energy (J) or electrical power(J/s). For short periods of time when the wave power incident on the EKSis relatively constant, the numbers obtained for the efficiency ofelectrical power conversion and for the efficiency of wave powerdissipation would be equal to that of efficiency of electrical energyconversion, and the efficiency of wave energy dissipation.

This calculation can be run by a program executed by a hardwareprocessor and stored on a computer-readable storage medium. Further, thecalculation can be performed for any EKS apparatus, be it a single WECalone in isolation, a linear row of WEC repeating units, or a mesh ofWEC units of any arbitrary geometric shape or density of packing. Thoughto repeat, for meshes of more than a few rows or very densely packedarrays such as those of FIGS. 13 A, C, D, and F, more complexmathematical techniques should be employed. There is no need to correctfor the angle of incidence between the wave propagation direction andthe orientation of the array with respect to that direction forcomputation of the electrical power (energy) conversion efficiency foran individual WEC because that quantity is dependent upon the individualWEC repeating units that are omni-directional with respect to the wavesbecause of their circular cross-section on the surface of the water.However, for computation of the efficiency of wave power (energy)dissipation of the EKS array as a whole, one merely has to know themaximal cross section diameter of the region of ocean encompassed by thearray in the direction that is perpendicular to the direction of wavepropagation.

The efficiency of electrical power transfer to the load of the WECrepeating component EKS apparatus can be increased and be maximized to asignificantly high number, to as high as 90%, if, for each WEC unit, theload resistance that that WEC sees and thus for the EKS apparatus as awhole is made significantly higher than the combined internal resistanceof all of the FCA coils of each of the WEC units composing the EKS, asituation in which a PCC circuit that delivers a higher voltage at alower current would usually be used. However, the power outputtransferred to the load in this situation will not be a maximum inmagnitude even as the efficiency might be quite high as per theconstraints of the maximum power theorem. There are applications,however, that might involve somewhat lower generated voltages andsomewhat higher generated currents where it might be desired to have themaximum electrical output be generated and delivered to the load eventhough the efficiency will be at a maximum of 50% as a result of theconstraints of the maximal power theorem with the other 50% of theoutput power being wasted due to ohmic i squared r losses in the coilwindings. Which option is chosen depends upon what is desired to be donewith the electric power generated.

In the exemplary embodiments described herein, optimization of the totalamount of wave kinetic energy dissipated via the most efficientproduction of electrical energy by each VLEG in each WEC repeatingcomponent of the EKS can be facilitated by optimization of thetremendous number of design parameters involving the coils of the FCA,the magnets of the PMA, the spring suspension system of series connectedsprings connected between three masses, the power collection circuitry,considerations regarding resonance frequency and mechanical impedancematching of the apparatus to that of the incoming waves to the closestextent possible, matching the electromagnetic damping factor as closelyas possible to that of the parasitic damping factor, and the geometry ofthe component parts of the VLEG structure that have been discussed inthe detailed description provided above.

In accordance with preferred embodiments, parasitic damping is minimizedand hence the efficiency of the wave kinetic energy dissipationconversion process to electrical energy of the VLEG being enhanced in anadvantageous decreased manner due to the mechanical configuration of thepreferred exemplary WEC repeating components of the EKS embodimentswhich exhibit remarkable mechanical simplicity for wave energy converterdevices; there are only two moving parts—a vibrating magnet or coppercoil rotor suspended by springs and a floating buoy collar that vibrateswith the incoming waves via a single sliding joint. There is no need forcomplex mechanical systems that intervene between the incident waveoscillation and the relative movement of the rotor with respect to thestator, in contrast to known WEC devices. The moving rotor is thecomponent that directly converts the linear kinetic energy of ocean wavemotion into electrical energy with a remarkable simplicity. There is noneed for intermediate energy conversion components such as hydraulicsystems, linear to rotary motion converters, bearing roller systems, aircolumn compression systems, pump systems, separations of the rotor andthe stator into different containment structure configurations, complexmultiple hinge assembly systems, flywheel systems and other similarcomponents. Hence, the survivability and durability in difficult marineenvironments including storms are enhanced.

For a given efficiency designed into the VLEG and the WEC repeatingcomponent of the EKS, the energy dissipation capacity of the presentprinciples can be enhanced by varying the geometric shape of the arrayfrom a seawall to a geometric mesh energy dissipating platform whosedensity of WEC's can be made extremely high, especially if smaller WEC'sare used to “carpet” a region of wave turbulent ocean without the needfor any steering mechanism. It is believed that such geometricalversatility is a novel feature; embodiments of the present principlesdescribed herein may be applicable to all geometric shapes includingcircles, squares and higher order polygons, linear and ring arrays withthe choice of design being dictated by whether the primary function isto protect structures behind an electrokinetic seawall and produceelectricity as a byproduct of the dissipation of deleterious ocean waveenergy or to use the WEC for the primary purpose of ocean wave powerconversion to electrical energy via geometric mesh embodiments that arecapable of being positioned, operated and monitored by remote means atpoints far out into the ocean away from environmentally sensitiveshorelines.

It will be further appreciated by those skilled in the art that thefigures representing the present principles are purely illustrative, andthe exemplary EKS apparatuses and VLEGs may be implemented in any numberof ways, including the protective and desirable dissipation of kineticwave energy of ocean waves via conversion into useful electrical energy;furthermore, the functionality of the present principles as it relatesto dissipating kinetic energy via the vibrational energy electrokineticmatrix transducer and its associated power collection circuitry may beextended to all forms of vibrational energy sources in the environmentover a wide magnitude of vibrational amplitudes and to all applicationswhere such vibrational energy sources may exist within the environmentof oceans, other bodies of water, and in other spatial regions andenvironments, and which may be harvested using means as describedherein.

Having described preferred embodiments of linear faraday inductiongenerators, as well as various exemplary arrangements thereof, which areintended to be illustrative and not limiting, it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope of the invention as outlined by the appended claims.Having thus described aspects of the invention, with the details andparticularity required by the patent laws, what is claimed and desiredprotected by Letters Patent is set forth in the appended claims.

What is claimed is:
 1. A linear generator, comprising: a permanentmagnet array having at least two magnets arranged end-to-end; a set ofconductive coils arranged around the permanent magnet array; afour-phase full wave rectifier configured to accept alternating currentinputs from the set of conductive coils and to produce one or moredirect current outputs; and a summing circuit configured to aggregatethe one or more direct current outputs from the rectifier to produce acombined, rectified direct current output.
 2. The linear generator ofclaim 1, wherein the four-phase full wave rectifier comprises Schottkydiodes.
 3. The linear generator of claim 1, wherein the four-phase fullwave rectifier is a bridge rectifier, wherein a first end of eachconductive coil in the set of conductive coils is tied together and asecond end of each conductive coil feeds a rectifier diode network. 4.The linear generator of claim 1, wherein the four-phase full waverectifier comprises two full wave center tapped rectifier circuits, afirst tapped rectifier circuit configured to separate out a positivehalf cycle for each phase and a second tapped rectifier circuitconfigured to separate out a negative half cycle for each phase.
 5. Thelinear generator of claim 4, wherein the four-phase full wave rectifierproduces a bipolar output.
 6. The linear generator of claim 1, whereinthe summing circuit is a current summing circuit with a plurality ofinputs.
 7. The linear generator of claim 6, wherein the current summingcircuit comprises a set of monolithic direct current to direct currentvoltage converters connected in series between a pair of currentsteering Schottky diodes.
 8. The linear generator of claim 1, whereinthe summing circuit is a voltage summing circuit with a plurality ofinputs.
 9. The linear generator of claim 1, comprising a plurality ofsets of conductive coils and a respective rectifier for each set ofconductive coils.
 10. The linear generator of claim 9, wherein thesumming circuit receives inputs from each of the rectifiers.
 11. Thelinear generator of claim 1, wherein the set of conductive coilscomprises four subsets of a plurality of conductive coils, with eachcoil being electrically connected in series with the other coils in therespective subset of coils, to the four-phase full-wave rectifier. 12.The linear generator of claim 1, wherein the set of conductive coilscomprises a plurality of subsets of four conductive coils, with eachsubset of four conductive coils feeding a respective four-phase fullwave rectifier circuit and summing circuit.
 13. The linear generator ofclaim 12, further comprising a second-layer summing circuit configuredto sum outputs of each of the respective summing circuits for therespective subsets of four conductive coils.
 14. The linear generator ofclaim 13, wherein the second-layer summing circuit is a summing circuitwith a plurality of inputs configured to produce a single direct currentoutput.
 15. An array of linear generators, comprising: a plurality ofindividual linear generators, each having a single direct current outputand each comprising: a permanent magnet array having at least twomagnets arranged end-to-end; a set of conductive coils arranged aroundthe permanent magnet array, the set comprising four subsets of aplurality of conductive coils, with each coil being electricallyconnected in series with the other coils in the respective subset ofcoils; a four-phase full wave rectifier configured to accept alternatingcurrent inputs from each subset of conductive coils and to produce oneor more direct current outputs; and a summing circuit configured toaggregate the one or more direct current outputs from the rectifier toproduce a combined, rectified direct current output.
 16. The array oflinear generators of claim 15, further comprising an array-level summingcircuit configured to aggregate the single direct current outputs of theplurality of individual linear generators to produce a single directcurrent output for the array.
 17. A system of generator arrays,comprising: a plurality of arrays of linear generators as recited inclaim 16; and a system-level summing circuit configured to aggregate thesingle direct current outputs for the plurality of arrays to produce asingle direct current system output.
 18. An array of linear generators,comprising: a plurality of individual linear generators, each having asingle direct current output and each comprising: a permanent magnetarray having at least two magnets arranged end-to-end; a set ofconductive coils arranged around the permanent magnet array, the setcomprising a plurality of subsets of four conductive coils each; aplurality of four-phase full wave rectifiers configured to acceptalternating current inputs from a respective subset of four conductivecoils and to produce one or more direct current outputs; and a summingcircuit configured to aggregate the one or more direct current outputsfrom the rectifiers to produce a combined, rectified direct currentoutput.
 19. The array of linear generators of claim 18, furthercomprising an array-level summing circuit configured to aggregate thesingle direct current outputs of the plurality of individual lineargenerators to produce a single direct current output for the array. 20.A system of generator arrays, comprising: a plurality of arrays oflinear generators as recited in claim 19; and a system-level summingcircuit configured to aggregate the single direct current outputs forthe plurality of arrays to produce a single direct current systemoutput.